LMFDB - Embedded newform 38.8.e.b.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	38.9
Dual form			38.8.e.b.17.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 - 7.87846i) q^{2} +(37.7512 - 31.6770i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-192.429 - 70.0383i) q^{5} +(-302.010 - 253.416i) q^{6} +(-814.928 + 1411.50i) q^{7} +(256.000 + 443.405i) q^{8} +(41.9510 - 237.916i) q^{9} +O(q^{10})$	\(q+(-1.38919 - 7.87846i) q^{2} +(37.7512 - 31.6770i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-192.429 - 70.0383i) q^{5} +(-302.010 - 253.416i) q^{6} +(-814.928 + 1411.50i) q^{7} +(256.000 + 443.405i) q^{8} +(41.9510 - 237.916i) q^{9} +(-284.475 + 1613.34i) q^{10} +(-1687.55 - 2922.93i) q^{11} +(-1576.98 + 2731.41i) q^{12} +(-6311.72 - 5296.16i) q^{13} +(12252.5 + 4459.55i) q^{14} +(-9483.02 + 3451.54i) q^{15} +(3137.72 - 2632.86i) q^{16} +(6352.22 + 36025.2i) q^{17} -1932.69 q^{18} +(22655.0 - 19509.6i) q^{19} +13105.8 q^{20} +(13947.5 + 79100.2i) q^{21} +(-20683.9 + 17355.8i) q^{22} +(-102048. + 37142.3i) q^{23} +(23710.1 + 8629.75i) q^{24} +(-27723.8 - 23263.0i) q^{25} +(-32957.4 + 57084.0i) q^{26} +(47935.7 + 83027.0i) q^{27} +(18113.4 - 102726. i) q^{28} +(6900.69 - 39135.8i) q^{29} +(40366.5 + 69916.8i) q^{30} +(54036.9 - 93594.6i) q^{31} +(-25101.7 - 21062.9i) q^{32} +(-156297. - 56887.4i) q^{33} +(274999. - 100091. i) q^{34} +(255674. - 214536. i) q^{35} +(2684.86 + 15226.6i) q^{36} -408636. q^{37} +(-185177. - 151384. i) q^{38} -406041. q^{39} +(-18206.4 - 103254. i) q^{40} +(-5269.18 + 4421.36i) q^{41} +(603812. - 219770. i) q^{42} +(-95849.5 - 34886.4i) q^{43} +(165471. + 138847. i) q^{44} +(-24735.8 + 42843.6i) q^{45} +(434387. + 752381. i) q^{46} +(124000. - 703238. i) q^{47} +(35051.5 - 198787. i) q^{48} +(-916445. - 1.58733e6i) q^{49} +(-144763. + 250737. i) q^{50} +(1.38098e6 + 1.15878e6i) q^{51} +(495518. + 180354. i) q^{52} +(-1.10509e6 + 402218. i) q^{53} +(587534. - 492999. i) q^{54} +(120017. + 680649. i) q^{55} -834487. q^{56} +(237247. - 1.45415e6i) q^{57} -317916. q^{58} +(190926. + 1.08279e6i) q^{59} +(494760. - 415153. i) q^{60} +(1.65728e6 - 603201. i) q^{61} +(-812449. - 295707. i) q^{62} +(301630. + 253098. i) q^{63} +(-131072. + 227023. i) q^{64} +(843621. + 1.46119e6i) q^{65} +(-231060. + 1.31041e6i) q^{66} +(-385359. + 2.18548e6i) q^{67} +(-1.17059e6 - 2.02752e6i) q^{68} +(-2.67586e6 + 4.63473e6i) q^{69} +(-2.04540e6 - 1.71629e6i) q^{70} +(-4.15172e6 - 1.51110e6i) q^{71} +(116232. - 42305.2i) q^{72} +(-328198. + 275391. i) q^{73} +(567671. + 3.21942e6i) q^{74} -1.78351e6 q^{75} +(-935427. + 1.66921e6i) q^{76} +5.50094e6 q^{77} +(564067. + 3.19898e6i) q^{78} +(628607. - 527464. i) q^{79} +(-788188. + 286877. i) q^{80} +(4.93616e6 + 1.79662e6i) q^{81} +(42153.4 + 35370.9i) q^{82} +(532018. - 921481. i) q^{83} +(-2.57025e6 - 4.45181e6i) q^{84} +(1.30080e6 - 7.37719e6i) q^{85} +(-141698. + 803610. i) q^{86} +(-979195. - 1.69602e6i) q^{87} +(864027. - 1.49654e6i) q^{88} +(5.64701e6 + 4.73840e6i) q^{89} +(371905. + 135362. i) q^{90} +(1.26191e7 - 4.59298e6i) q^{91} +(5.32416e6 - 4.46750e6i) q^{92} +(-924841. - 5.24504e6i) q^{93} -5.71269e6 q^{94} +(-5.72589e6 + 2.16749e6i) q^{95} -1.61483e6 q^{96} +(634897. + 3.60068e6i) q^{97} +(-1.12326e7 + 9.42527e6i) q^{98} +(-766205. + 278876. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) $ 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38919	−	7.87846i	−0.122788	−	0.696364i
$2$	−1.38919	−	7.87846i	−0.122788	−	0.696364i
$3$	37.7512	−	31.6770i	0.807247	−	0.677360i	−0.142702	−	0.989766i	$-0.545579\pi$
$3$	37.7512	−	31.6770i	0.807247	−	0.677360i	0.949949	+	0.312405i	$0.101135\pi$
$4$	−60.1403	+	21.8893i	−0.469846	+	0.171010i
$5$	−192.429	−	70.0383i	−0.688454	−	0.250577i	−0.0259807	−	0.999662i	$-0.508271\pi$
$5$	−192.429	−	70.0383i	−0.688454	−	0.250577i	−0.662473	+	0.749086i	$0.730493\pi$
$6$	−302.010	−	253.416i	−0.570810	−	0.478966i
$7$	−814.928	+	1411.50i	−0.898000	+	1.55538i	−0.0679524	+	0.997689i	$0.521647\pi$
$7$	−814.928	+	1411.50i	−0.898000	+	1.55538i	−0.830047	+	0.557693i	$0.811687\pi$
$8$	256.000	+	443.405i	0.176777	+	0.306186i
$9$	41.9510	−	237.916i	0.0191820	−	0.108786i
$10$	−284.475	+	1613.34i	−0.0899589	+	0.510182i
$11$	−1687.55	−	2922.93i	−0.382281	−	0.662131i	0.609107	−	0.793088i	$-0.291528\pi$
$11$	−1687.55	−	2922.93i	−0.382281	−	0.662131i	−0.991388	+	0.130958i	$0.958195\pi$
$12$	−1576.98	+	2731.41i	−0.263446	+	0.456303i
$13$	−6311.72	−	5296.16i	−0.796793	−	0.668589i	0.150624	−	0.988591i	$-0.451872\pi$
$13$	−6311.72	−	5296.16i	−0.796793	−	0.668589i	−0.947417	+	0.320002i	$0.896316\pi$
$14$	12252.5	+	4459.55i	1.19338	+	0.434353i
$15$	−9483.02	+	3451.54i	−0.725483	+	0.264054i
$16$	3137.72	−	2632.86i	0.191511	−	0.160697i
$17$	6352.22	+	36025.2i	0.313584	+	1.77842i	0.580051	+	0.814580i	$0.303033\pi$
$17$	6352.22	+	36025.2i	0.313584	+	1.77842i	−0.266466	+	0.963844i	$0.585856\pi$
$18$	−1932.69			−0.0781102
$19$	22655.0	−	19509.6i	0.757750	−	0.652545i
$19$	22655.0	−	19509.6i	0.757750	−	0.652545i
$20$	13105.8			0.366319
$21$	13947.5	+	79100.2i	0.328646	+	1.86385i
$22$	−20683.9	+	17355.8i	−0.414145	+	0.347509i
$23$	−102048.	+	37142.3i	−1.74886	+	0.636534i	−0.999667	−	0.0258153i	$-0.991782\pi$
$23$	−102048.	+	37142.3i	−1.74886	+	0.636534i	−0.749195	+	0.662349i	$0.769560\pi$
$24$	23710.1	+	8629.75i	0.350101	+	0.127426i
$25$	−27723.8	−	23263.0i	−0.354865	−	0.297767i
$26$	−32957.4	+	57084.0i	−0.367745	+	0.636953i
$27$	47935.7	+	83027.0i	0.468690	+	0.811795i
$28$	18113.4	−	102726.i	0.155936	−	0.884357i
$29$	6900.69	−	39135.8i	0.0525412	−	0.297976i	−0.947202	−	0.320637i	$-0.896103\pi$
$29$	6900.69	−	39135.8i	0.0525412	−	0.297976i	0.999743	+	0.0226616i	$0.00721402\pi$
$30$	40366.5	+	69916.8i	0.272958	+	0.472778i
$31$	54036.9	−	93594.6i	0.325780	−	0.564267i	−0.655890	−	0.754857i	$-0.727706\pi$
$31$	54036.9	−	93594.6i	0.325780	−	0.564267i	0.981670	+	0.190589i	$0.0610398\pi$
$32$	−25101.7	−	21062.9i	−0.135419	−	0.113630i
$33$	−156297.	−	56887.4i	−0.757097	−	0.275561i
$34$	274999.	−	100091.i	1.19993	−	0.436738i
$35$	255674.	−	214536.i	1.00797	−	0.845790i
$36$	2684.86	+	15226.6i	0.00959098	+	0.0543932i
$37$	−408636.			−1.32626			−0.663132	−	0.748502i	$-0.730773\pi$
$37$	−408636.			−1.32626			−0.663132	+	0.748502i	$0.730773\pi$
$38$	−185177.	−	151384.i	−0.547451	−	0.447546i
$39$	−406041.			−1.09608
$40$	−18206.4	−	103254.i	−0.0449795	−	0.255091i
$41$	−5269.18	+	4421.36i	−0.0119399	+	0.0100187i	−0.648738	−	0.761012i	$-0.724703\pi$
$41$	−5269.18	+	4421.36i	−0.0119399	+	0.0100187i	0.636798	+	0.771031i	$0.280258\pi$
$42$	603812.	−	219770.i	1.25756	−	0.457715i
$43$	−95849.5	−	34886.4i	−0.183844	−	0.0669139i	0.248458	−	0.968643i	$-0.420076\pi$
$43$	−95849.5	−	34886.4i	−0.183844	−	0.0669139i	−0.432302	+	0.901729i	$0.642299\pi$
$44$	165471.	+	138847.i	0.292844	+	0.245726i
$45$	−24735.8	+	42843.6i	−0.0404652	+	0.0700878i
$46$	434387.	+	752381.i	0.657998	+	1.13969i
$47$	124000.	−	703238.i	0.174212	−	0.988007i	−0.764837	−	0.644224i	$-0.777180\pi$
$47$	124000.	−	703238.i	0.174212	−	0.988007i	0.939049	−	0.343783i	$-0.111708\pi$
$48$	35051.5	−	198787.i	0.0457470	−	0.259444i
$49$	−916445.	−	1.58733e6i	−1.11281	−	1.92744i
$50$	−144763.	+	250737.i	−0.163781	+	0.283677i
$51$	1.38098e6	+	1.15878e6i	1.45777	+	1.22322i
$52$	495518.	+	180354.i	0.488706	+	0.177874i
$53$	−1.10509e6	+	402218.i	−1.01960	+	0.371105i	−0.797113	−	0.603831i	$-0.793640\pi$
$53$	−1.10509e6	+	402218.i	−1.01960	+	0.371105i	−0.222489	+	0.974935i	$0.571418\pi$
$54$	587534.	−	492999.i	0.507755	−	0.426057i
$55$	120017.	+	680649.i	0.0972685	+	0.551637i
$56$	−834487.			−0.634982
$57$	237247.	−	1.45415e6i	0.169683	−	1.04003i
$58$	−317916.			−0.213951
$59$	190926.	+	1.08279e6i	0.121027	+	0.686379i	0.983588	+	0.180426i	$0.0577478\pi$
$59$	190926.	+	1.08279e6i	0.121027	+	0.686379i	−0.862561	+	0.505952i	$0.831141\pi$
$60$	494760.	−	415153.i	0.295710	−	0.248130i
$61$	1.65728e6	−	603201.i	0.934850	−	0.340257i	0.170720	−	0.985320i	$-0.445391\pi$
$61$	1.65728e6	−	603201.i	0.934850	−	0.340257i	0.764130	+	0.645062i	$0.223169\pi$
$62$	−812449.	−	295707.i	−0.432937	−	0.157576i
$63$	301630.	+	253098.i	0.151979	+	0.127525i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	843621.	+	1.46119e6i	0.381023	+	0.659950i
$66$	−231060.	+	1.31041e6i	−0.0989283	+	0.561050i
$67$	−385359.	+	2.18548e6i	−0.156532	+	0.887738i	0.800840	+	0.598879i	$0.204387\pi$
$67$	−385359.	+	2.18548e6i	−0.156532	+	0.887738i	−0.957372	+	0.288859i	$0.906724\pi$
$68$	−1.17059e6	−	2.02752e6i	−0.451465	−	0.781960i
$69$	−2.67586e6	+	4.63473e6i	−0.980600	+	1.69845i
$70$	−2.04540e6	−	1.71629e6i	−0.712745	−	0.598064i
$71$	−4.15172e6	−	1.51110e6i	−1.37665	−	0.501060i	−0.455490	−	0.890241i	$-0.650536\pi$
$71$	−4.15172e6	−	1.51110e6i	−1.37665	−	0.501060i	−0.921162	+	0.389180i	$0.872758\pi$
$72$	116232.	−	42305.2i	0.0366998	−	0.0133576i
$73$	−328198.	+	275391.i	−0.0987429	+	0.0828552i	−0.690823	−	0.723024i	$-0.742751\pi$
$73$	−328198.	+	275391.i	−0.0987429	+	0.0828552i	0.592080	+	0.805879i	$0.298307\pi$
$74$	567671.	+	3.21942e6i	0.162849	+	0.923563i
$75$	−1.78351e6			−0.488159
$76$	−935427.	+	1.66921e6i	−0.244434	+	0.436179i
$77$	5.50094e6			1.37315
$78$	564067.	+	3.19898e6i	0.134586	+	0.763274i
$79$	628607.	−	527464.i	0.143445	−	0.120364i	−0.568242	−	0.822862i	$-0.692376\pi$
$79$	628607.	−	527464.i	0.143445	−	0.120364i	0.711686	+	0.702497i	$0.247932\pi$
$80$	−788188.	+	286877.i	−0.172113	+	0.0626442i
$81$	4.93616e6	+	1.79662e6i	1.03203	+	0.375628i
$82$	42153.4	+	35370.9i	0.00844275	+	0.00708431i
$83$	532018.	−	921481.i	0.102130	−	0.176894i	−0.810432	−	0.585833i	$-0.800768\pi$
$83$	532018.	−	921481.i	0.102130	−	0.176894i	0.912562	+	0.408939i	$0.134101\pi$
$84$	−2.57025e6	−	4.45181e6i	−0.473150	−	0.819519i
$85$	1.30080e6	−	7.37719e6i	0.229743	−	1.30294i
$86$	−141698.	+	803610.i	−0.0240226	+	0.136239i
$87$	−979195.	−	1.69602e6i	−0.159423	−	0.276129i
$88$	864027.	−	1.49654e6i	0.135157	−	0.234099i
$89$	5.64701e6	+	4.73840e6i	0.849089	+	0.712470i	0.959589	−	0.281406i	$-0.0908007\pi$
$89$	5.64701e6	+	4.73840e6i	0.849089	+	0.712470i	−0.110500	+	0.993876i	$0.535245\pi$
$90$	371905.	+	135362.i	0.0537753	+	0.0195726i
$91$	1.26191e7	−	4.59298e6i	1.75543	−	0.638925i
$92$	5.32416e6	−	4.46750e6i	0.712843	−	0.598146i
$93$	−924841.	−	5.24504e6i	−0.119228	−	0.676173i
$94$	−5.71269e6			−0.709404
$95$	−5.72589e6	+	2.16749e6i	−0.685189	+	0.259372i
$96$	−1.61483e6			−0.186285
$97$	634897.	+	3.60068e6i	0.0706321	+	0.400574i	0.999542	+	0.0302682i	$0.00963613\pi$
$97$	634897.	+	3.60068e6i	0.0706321	+	0.400574i	−0.928910	+	0.370306i	$0.879253\pi$
$98$	−1.12326e7	+	9.42527e6i	−1.20556	+	1.01159i
$99$	−766205.	+	278876.i	−0.0793637	+	0.0288860i
$100$	2.17653e6	+	792192.i	0.217653	+	0.0792192i
$101$	−6.48977e6	−	5.44556e6i	−0.626764	−	0.525918i	0.273157	−	0.961969i	$-0.411932\pi$
$101$	−6.48977e6	−	5.44556e6i	−0.626764	−	0.525918i	−0.899922	+	0.436052i	$0.856377\pi$
$102$	7.21094e6	−	1.24897e7i	0.672808	−	1.16534i
$103$	−5.49355e6	−	9.51511e6i	−0.495362	−	0.857992i	0.504624	−	0.863339i	$-0.331631\pi$
$103$	−5.49355e6	−	9.51511e6i	−0.495362	−	0.857992i	−0.999986	+	0.00534713i	$0.998298\pi$
$104$	732544.	−	4.15446e6i	0.0638582	−	0.362158i
$105$	2.85615e6	−	1.61980e7i	0.240779	−	1.36552i
$106$	4.70403e6	+	8.14762e6i	0.383619	+	0.664447i
$107$	−5.47519e6	+	9.48331e6i	−0.432072	+	0.748371i	−0.997052	−	0.0767342i	$-0.975551\pi$
$107$	−5.47519e6	+	9.48331e6i	−0.432072	+	0.748371i	0.564980	+	0.825105i	$0.308884\pi$
$108$	−4.70027e6	−	3.94399e6i	−0.359037	−	0.301268i
$109$	8.79429e6	+	3.20086e6i	0.650441	+	0.236741i	0.646104	−	0.763249i	$-0.276397\pi$
$109$	8.79429e6	+	3.20086e6i	0.650441	+	0.236741i	0.00433703	+	0.999991i	$0.498619\pi$
$110$	5.19574e6	−	1.89109e6i	0.372197	−	0.135469i
$111$	−1.54265e7	+	1.29444e7i	−1.07062	+	0.898359i
$112$	1.15926e6	+	6.57447e6i	0.0779680	+	0.442179i
$113$	9.80115e6			0.639002			0.319501	−	0.947586i	$-0.396485\pi$
$113$	9.80115e6			0.639002			0.319501	+	0.947586i	$0.396485\pi$
$114$	−1.17861e7	+	150942.i	−0.745078	+	0.00954209i
$115$	2.22383e7			1.36351
$116$	441644.	+	2.50469e6i	0.0262706	+	0.148988i
$117$	−1.52482e6	+	1.27948e6i	−0.0880174	+	0.0738554i
$118$	8.26552e6	−	3.00840e6i	0.463109	−	0.168558i
$119$	−5.60261e7	−	2.03918e7i	−3.04773	−	1.10928i
$120$	−3.95808e6	−	3.32122e6i	−0.209098	−	0.175454i
$121$	4.04791e6	−	7.01119e6i	0.207722	−	0.359785i
$122$	−7.05457e6	−	1.22189e7i	−0.351731	−	0.609216i
$123$	−58862.1	+	333824.i	−0.00285212	+	0.0161752i
$124$	−1.20108e6	+	6.81164e6i	−0.0565711	+	0.320831i
$125$	1.17047e7	+	2.02731e7i	0.536013	+	0.928402i
$126$	1.57500e6	−	2.72798e6i	0.0701430	−	0.121491i
$127$	3.31066e7	+	2.77797e7i	1.43417	+	1.20341i	0.943195	+	0.332240i	$0.107804\pi$
$127$	3.31066e7	+	2.77797e7i	1.43417	+	1.20341i	0.490977	+	0.871173i	$0.336640\pi$
$128$	1.97068e6	+	717268.i	0.0830579	+	0.0302306i
$129$	−4.72353e6	+	1.71922e6i	−0.193733	+	0.0705129i
$130$	1.03400e7	−	8.67631e6i	0.412781	−	0.346364i
$131$	2.80442e6	+	1.59047e7i	0.108992	+	0.618123i	0.989551	+	0.144186i	$0.0460565\pi$
$131$	2.80442e6	+	1.59047e7i	0.108992	+	0.618123i	−0.880559	+	0.473937i	$0.842832\pi$
$132$	1.06450e7			0.402843
$133$	9.07553e6	+	4.78763e7i	0.334496	+	1.76458i
$134$	1.77535e7			0.637409
$135$	−3.40913e6	−	1.93341e7i	−0.119255	−	0.676326i
$136$	−1.43476e7	+	1.20391e7i	−0.489095	+	0.410399i
$137$	4.24406e6	−	1.54471e6i	0.141013	−	0.0513246i	−0.270549	−	0.962706i	$-0.587205\pi$
$137$	4.24406e6	−	1.54471e6i	0.141013	−	0.0513246i	0.411563	+	0.911381i	$0.364983\pi$
$138$	4.02318e7	+	1.46432e7i	1.30315	+	0.474306i
$139$	−1.17903e7	−	9.89327e6i	−0.372370	−	0.312456i	0.437328	−	0.899302i	$-0.355925\pi$
$139$	−1.17903e7	−	9.89327e6i	−0.372370	−	0.312456i	−0.809698	+	0.586846i	$0.800369\pi$
$140$	−1.06803e7	+	1.84988e7i	−0.328954	+	0.569765i
$141$	−1.75953e7	−	3.04760e7i	−0.528604	−	0.915570i
$142$	−6.13766e6	+	3.48084e7i	−0.179884	+	1.02018i
$143$	−4.82893e6	+	2.73862e7i	−0.138094	+	0.783170i
$144$	−494768.	−	856963.i	−0.0138081	−	0.0239163i
$145$	−4.06890e6	+	7.04753e6i	−0.110838	+	0.191977i
$146$	2.62558e6	+	2.20313e6i	0.0698218	+	0.0585874i
$147$	−8.48787e7	−	3.08933e7i	−2.20388	−	0.802147i
$148$	2.45755e7	−	8.94474e6i	0.623140	−	0.226805i
$149$	−589564.	+	494703.i	−0.0146009	+	0.0122516i	−0.650059	−	0.759884i	$-0.725256\pi$
$149$	−589564.	+	494703.i	−0.0146009	+	0.0122516i	0.635458	+	0.772135i	$0.280811\pi$
$150$	2.47763e6	+	1.40513e7i	0.0599399	+	0.339936i
$151$	−6.49057e7			−1.53413			−0.767067	−	0.641567i	$-0.778285\pi$
$151$	−6.49057e7			−1.53413			−0.767067	+	0.641567i	$0.778285\pi$
$152$	1.44503e7	+	5.05088e6i	0.333753	+	0.116658i
$153$	8.83745e6			0.199483
$154$	−7.64183e6	−	4.33389e7i	−0.168607	−	0.956216i
$155$	−1.69535e7	+	1.42256e7i	−0.365677	+	0.306839i
$156$	2.44195e7	−	8.88795e6i	0.514991	−	0.187441i
$157$	6.26966e7	+	2.28197e7i	1.29299	+	0.470610i	0.894707	−	0.446653i	$-0.147384\pi$
$157$	6.26966e7	+	2.28197e7i	1.29299	+	0.470610i	0.398282	+	0.917263i	$0.369606\pi$
$158$	−5.02886e6	−	4.21971e6i	−0.101431	−	0.0851105i
$159$	−2.89772e7	+	5.01900e7i	−0.571698	+	0.990211i
$160$	3.35509e6	+	5.81118e6i	0.0647566	+	0.112162i
$161$	3.07353e7	−	1.74308e8i	0.580425	−	3.29175i
$162$	7.29733e6	−	4.13852e7i	0.134853	−	0.764790i
$163$	4.95247e6	+	8.57793e6i	0.0895705	+	0.155141i	0.907330	−	0.420420i	$-0.138117\pi$
$163$	4.95247e6	+	8.57793e6i	0.0895705	+	0.155141i	−0.817759	+	0.575561i	$0.804784\pi$
$164$	220109.	−	381241.i	0.00389659	−	0.00674910i
$165$	2.60917e7	+	2.18935e7i	0.452177	+	0.379421i
$166$	−7.99893e6	−	2.91137e6i	−0.135723	−	0.0493991i
$167$	7.99504e6	−	2.90996e6i	0.132835	−	0.0483480i	−0.274747	−	0.961516i	$-0.588594\pi$
$167$	7.99504e6	−	2.90996e6i	0.132835	−	0.0483480i	0.407582	+	0.913168i	$0.366372\pi$
$168$	−3.15029e7	+	2.64340e7i	−0.512587	+	0.430112i
$169$	892294.	+	5.06045e6i	0.0142202	+	0.0806466i
$170$	−5.99279e7			−0.935531
$171$	−3.69124e6	−	6.20842e6i	−0.0564528	−	0.0949500i
$172$	6.52806e6			0.0978215
$173$	352418.	+	1.99866e6i	0.00517484	+	0.0293480i	0.987286	−	0.158955i	$-0.0508124\pi$
$173$	352418.	+	1.99866e6i	0.00517484	+	0.0293480i	−0.982111	+	0.188303i	$0.939701\pi$
$174$	−1.20017e7	+	1.00706e7i	−0.172711	+	0.144922i
$175$	5.54286e7	−	2.01744e7i	0.781809	−	0.284555i
$176$	−1.29907e7	−	4.72824e6i	−0.179613	−	0.0653740i
$177$	4.15074e7	+	3.48288e7i	0.562625	+	0.472098i
$178$	2.94866e7	−	5.10723e7i	0.391881	−	0.678758i
$179$	2.62038e7	+	4.53863e7i	0.341491	+	0.591479i	0.984710	−	0.174203i	$-0.0557349\pi$
$179$	2.62038e7	+	4.53863e7i	0.341491	+	0.591479i	−0.643219	+	0.765682i	$0.722402\pi$
$180$	549802.	−	3.11808e6i	0.00702671	−	0.0398505i
$181$	1.83057e7	−	1.03817e8i	0.229463	−	1.30135i	−0.624504	−	0.781022i	$-0.714699\pi$
$181$	1.83057e7	−	1.03817e8i	0.229463	−	1.30135i	0.853967	−	0.520327i	$-0.174190\pi$
$182$	−5.37159e7	−	9.30387e7i	−0.660470	−	1.14397i
$183$	4.34567e7	−	7.52693e7i	0.524177	−	0.907902i
$184$	−4.25933e7	−	3.57400e7i	−0.504056	−	0.422953i
$185$	7.86332e7	+	2.86201e7i	0.913072	+	0.332331i
$186$	−4.00380e7	+	1.45727e7i	−0.456223	+	0.166052i
$187$	9.45794e7	−	7.93616e7i	1.05767	−	0.887492i
$188$	7.93599e6	+	4.50072e7i	0.0871061	+	0.494003i
$189$	−1.56257e8			−1.68353
$190$	2.50308e7	+	4.21001e7i	0.264750	+	0.445293i
$191$	−8.25055e7			−0.856774			−0.428387	−	0.903595i	$-0.640918\pi$
$191$	−8.25055e7			−0.856774			−0.428387	+	0.903595i	$0.640918\pi$
$192$	2.24330e6	+	1.27224e7i	0.0228735	+	0.129722i
$193$	4.82429e6	−	4.04806e6i	0.0483040	−	0.0405319i	−0.618316	−	0.785930i	$-0.712185\pi$
$193$	4.82429e6	−	4.04806e6i	0.0483040	−	0.0405319i	0.666620	+	0.745398i	$0.267740\pi$
$194$	2.74858e7	−	1.00040e7i	0.270273	−	0.0983713i
$195$	7.81340e7	+	2.84384e7i	0.754604	+	0.274653i
$196$	8.98608e7	+	7.54022e7i	0.852460	+	0.715299i
$197$	2.48515e7	−	4.30440e7i	0.231590	−	0.401126i	−0.726686	−	0.686970i	$-0.758940\pi$
$197$	2.48515e7	−	4.30440e7i	0.231590	−	0.401126i	0.958276	+	0.285843i	$0.0922737\pi$
$198$	3.26151e6	+	5.64911e6i	0.0298601	+	0.0517192i
$199$	−2.85986e7	+	1.62191e8i	−0.257252	+	1.45895i	0.532974	+	0.846132i	$0.321074\pi$
$199$	−2.85986e7	+	1.62191e8i	−0.257252	+	1.45895i	−0.790226	+	0.612816i	$0.790037\pi$
$200$	3.21765e6	−	1.82482e7i	0.0284403	−	0.161293i
$201$	5.46817e7	+	9.47114e7i	0.474958	+	0.822652i
$202$	−3.38872e7	+	5.86943e7i	−0.289271	+	0.501033i
$203$	4.96165e7	+	4.16332e7i	0.416284	+	0.349304i
$204$	−1.08417e8	−	3.94606e7i	−0.894113	−	0.325430i
$205$	1.32361e6	−	481753.i	0.0107305	−	0.00390558i
$206$	−6.73329e7	+	5.64990e7i	−0.536651	+	0.450303i
$207$	4.55574e6	+	2.58369e7i	0.0356996	+	0.202462i
$208$	−3.37484e7			−0.260035
$209$	−9.52566e7	−	3.32954e7i	−0.721744	−	0.252274i
$210$	−1.31583e8			−0.980466
$211$	8.95612e6	+	5.07927e7i	0.0656344	+	0.372231i	0.999878	+	0.0155966i	$0.00496475\pi$
$211$	8.95612e6	+	5.07927e7i	0.0656344	+	0.372231i	−0.934244	+	0.356635i	$0.883924\pi$
$212$	5.76559e7	−	4.83791e7i	0.415593	−	0.348724i
$213$	−2.04600e8	+	7.44682e7i	−1.45070	+	0.528010i
$214$	8.23200e7	+	2.99620e7i	0.574192	+	0.208989i
$215$	1.60008e7	+	1.34263e7i	0.109801	+	0.0921342i
$216$	−2.45431e7	+	4.25098e7i	−0.165707	+	0.287013i
$217$	8.80724e7	+	1.52546e8i	0.585101	+	1.01342i
$218$	1.30009e7	−	7.37320e7i	0.0849919	−	0.482013i
$219$	−3.66631e6	+	2.07927e7i	−0.0235871	+	0.133769i
$220$	−2.21168e7	−	3.83073e7i	−0.140037	−	0.242551i
$221$	1.50702e8	−	2.61023e8i	0.939173	−	1.62670i
$222$	1.23412e8	+	1.03555e8i	0.757045	+	0.635236i
$223$	−4.11562e7	−	1.49796e7i	−0.248524	−	0.0904553i	0.214755	−	0.976668i	$-0.431105\pi$
$223$	−4.11562e7	−	1.49796e7i	−0.248524	−	0.0904553i	−0.463278	+	0.886213i	$0.653327\pi$
$224$	5.01863e7	−	1.82663e7i	0.298344	−	0.108588i
$225$	−6.69768e6	+	5.62002e6i	−0.0391999	+	0.0328927i
$226$	−1.36156e7	−	7.72180e7i	−0.0784617	−	0.444978i
$227$	−2.98335e8			−1.69283			−0.846415	−	0.532524i	$-0.821244\pi$
$227$	−2.98335e8			−1.69283			−0.846415	+	0.532524i	$0.821244\pi$
$228$	1.75622e7	+	9.26464e7i	0.0981313	+	0.517674i
$229$	2.20314e8			1.21232			0.606162	−	0.795341i	$-0.292708\pi$
$229$	2.20314e8			1.21232			0.606162	+	0.795341i	$0.292708\pi$
$230$	−3.08931e7	−	1.75203e8i	−0.167423	−	0.949500i
$231$	2.07667e8	−	1.74253e8i	1.10847	−	0.930120i
$232$	1.91196e7	−	6.95896e6i	0.100524	−	0.0365878i
$233$	−1.92917e8	−	7.02160e7i	−0.999136	−	0.363656i	−0.209885	−	0.977726i	$-0.567309\pi$
$233$	−1.92917e8	−	7.02160e7i	−0.999136	−	0.363656i	−0.789251	+	0.614070i	$0.789531\pi$
$234$	1.21986e7	+	1.02358e7i	0.0622377	+	0.0522236i
$235$	−7.31147e7	+	1.26638e8i	−0.367509	+	0.636543i
$236$	−3.51839e7	−	6.09404e7i	−0.174242	−	0.301796i
$237$	7.02219e6	−	3.98248e7i	0.0342652	−	0.194328i
$238$	−8.28257e7	+	4.69728e8i	−0.398241	+	2.25853i
$239$	2.62513e7	+	4.54686e7i	0.124382	+	0.215436i	0.921491	−	0.388399i	$-0.126972\pi$
$239$	2.62513e7	+	4.54686e7i	0.124382	+	0.215436i	−0.797109	+	0.603835i	$0.793638\pi$
$240$	−2.06676e7	+	3.57974e7i	−0.0965053	+	0.167152i
$241$	1.20823e7	+	1.01382e7i	0.0556019	+	0.0466555i	0.670165	−	0.742212i	$-0.266223\pi$
$241$	1.20823e7	+	1.01382e7i	0.0556019	+	0.0466555i	−0.614563	+	0.788868i	$0.710668\pi$
$242$	−6.08607e7	−	2.21515e7i	−0.276047	−	0.100473i
$243$	4.62315e7	−	1.68269e7i	0.206688	−	0.0752284i
$244$	−8.64658e7	+	7.25534e7i	−0.381048	+	0.319737i
$245$	6.51764e7	+	3.69634e8i	0.283145	+	1.60580i
$246$	2.71179e6			0.0116140
$247$	−2.46318e8	+	3.15455e6i	−1.04005	+	0.0133198i
$248$	5.53338e7			0.230361
$249$	−9.10548e6	−	5.16398e7i	−0.0373771	−	0.211976i
$250$	1.43461e8	−	1.20378e8i	0.580690	−	0.487257i
$251$	−2.25566e8	+	8.20994e7i	−0.900359	+	0.327704i	−0.750397	−	0.660988i	$-0.770138\pi$
$251$	−2.25566e8	+	8.20994e7i	−0.900359	+	0.327704i	−0.149963	+	0.988692i	$0.547915\pi$
$252$	−2.36803e7	−	8.61892e6i	−0.0932148	−	0.0339274i
$253$	2.80775e8	+	2.35598e8i	1.09003	+	0.914640i
$254$	1.72870e8	−	2.99420e8i	0.661915	−	1.14647i
$255$	−1.84581e8	−	3.19703e8i	−0.697100	−	1.20741i
$256$	2.91333e6	−	1.65223e7i	0.0108530	−	0.0615505i
$257$	−2.96301e7	+	1.68041e8i	−0.108885	+	0.617516i	0.880713	+	0.473651i	$0.157064\pi$
$257$	−2.96301e7	+	1.68041e8i	−0.108885	+	0.617516i	−0.989597	+	0.143865i	$0.954047\pi$
$258$	2.01067e7	+	3.48258e7i	0.0728906	+	0.126250i
$259$	3.33009e8	−	5.76788e8i	1.19099	−	2.06285i
$260$	−8.27202e7	−	6.94105e7i	−0.291880	−	0.244917i
$261$	−9.02153e6	−	3.28357e6i	−0.0314079	−	0.0114315i
$262$	1.21408e8	−	4.41891e7i	0.417056	−	0.151796i
$263$	−4.20520e8	+	3.52858e8i	−1.42542	+	1.19607i	−0.477056	+	0.878873i	$0.658296\pi$
$263$	−4.20520e8	+	3.52858e8i	−1.42542	+	1.19607i	−0.948361	+	0.317194i	$0.897259\pi$
$264$	−1.47878e7	−	8.38659e7i	−0.0494642	−	0.280525i
$265$	2.40821e8			0.794939
$266$	3.64584e8	−	1.38010e8i	1.18772	−	0.449600i
$267$	3.63280e8			1.16802
$268$	−2.46630e7	−	1.39871e8i	−0.0782661	−	0.443869i
$269$	−9.30251e7	+	7.80573e7i	−0.291385	+	0.244501i	−0.776748	−	0.629812i	$-0.783132\pi$
$269$	−9.30251e7	+	7.80573e7i	−0.291385	+	0.244501i	0.485363	+	0.874313i	$0.338688\pi$
$270$	−1.47587e8	+	5.37173e7i	−0.456326	+	0.166089i
$271$	−1.17433e8	−	4.27422e7i	−0.358425	−	0.130456i	0.156530	−	0.987673i	$-0.449969\pi$
$271$	−1.17433e8	−	4.27422e7i	−0.358425	−	0.130456i	−0.514955	+	0.857217i	$0.672191\pi$
$272$	1.14781e8	+	9.63125e7i	0.345842	+	0.290196i
$273$	3.30895e8	−	5.73126e8i	0.984284	−	1.70483i
$274$	−1.80657e7	−	3.12908e7i	−0.0530553	−	0.0918945i
$275$	−2.12108e7	+	1.20292e8i	−0.0615024	+	0.348797i
$276$	5.94763e7	−	3.37307e8i	0.170279	−	0.965703i
$277$	−3.01090e8	−	5.21503e8i	−0.851172	−	1.47427i	−0.880151	−	0.474693i	$-0.842559\pi$
$277$	−3.01090e8	−	5.21503e8i	−0.851172	−	1.47427i	0.0289791	−	0.999580i	$-0.490774\pi$
$278$	−6.15648e7	+	1.06633e8i	−0.171860	+	0.297671i
$279$	−2.00007e7	−	1.67826e7i	−0.0551355	−	0.0462642i
$280$	1.60579e8	+	5.84460e7i	0.437156	+	0.159112i
$281$	−1.44055e7	+	5.24319e6i	−0.0387309	+	0.0140969i	−0.361313	−	0.932445i	$-0.617671\pi$
$281$	−1.44055e7	+	5.24319e6i	−0.0387309	+	0.0140969i	0.322582	+	0.946542i	$0.395449\pi$
$282$	−2.15661e8	+	1.80961e8i	−0.572664	+	0.480522i
$283$	−9.64110e7	−	5.46774e8i	−0.252857	−	1.43402i	−0.801515	−	0.597974i	$-0.795973\pi$
$283$	−9.64110e7	−	5.46774e8i	−0.252857	−	1.43402i	0.548659	−	0.836046i	$-0.315139\pi$
$284$	2.82763e8			0.732501
$285$	−1.47500e8	+	2.63204e8i	−0.377428	+	0.673497i
$286$	2.22470e8			0.562328
$287$	−1.94674e6	−	1.10405e7i	−0.00486096	−	0.0275679i
$288$	−6.06423e6	+	5.08849e6i	−0.0149590	+	0.0125521i
$289$	−8.71874e8	+	3.17336e8i	−2.12477	+	0.773352i
$290$	6.11762e7	+	2.22663e7i	0.147295	+	0.0536112i
$291$	1.38027e8	+	1.15818e8i	0.328351	+	0.275519i
$292$	1.37098e7	−	2.37461e7i	0.0322249	−	0.0558152i
$293$	−5.91689e7	−	1.02484e8i	−0.137422	−	0.238022i	0.789098	−	0.614267i	$-0.210548\pi$
$293$	−5.91689e7	−	1.02484e8i	−0.137422	−	0.238022i	−0.926520	+	0.376245i	$0.877215\pi$
$294$	−1.25480e8	+	7.11630e8i	−0.287977	+	1.63320i
$295$	3.90975e7	−	2.21733e8i	0.0886690	−	0.502867i
$296$	−1.04611e8	−	1.81191e8i	−0.234453	−	0.406084i
$297$	1.61788e8	−	2.80225e8i	0.358343	−	0.620668i
$298$	4.71652e6	+	3.95763e6i	0.0103244	+	0.00866319i
$299$	8.40807e8	+	3.06029e8i	1.81906	+	0.662084i
$300$	1.07261e8	−	3.90397e7i	0.229360	−	0.0834800i
$301$	1.27352e8	−	1.06861e8i	0.269169	−	0.225859i
$302$	9.01660e7	+	5.11357e8i	0.188373	+	1.06832i
$303$	−4.17496e8			−0.862189
$304$	1.97190e7	−	1.20863e8i	0.0402557	−	0.246738i
$305$	−3.61156e8			−0.728861
$306$	−1.22769e7	−	6.96255e7i	−0.0244941	−	0.138913i
$307$	−1.56298e8	+	1.31150e8i	−0.308297	+	0.258692i	−0.783788	−	0.621029i	$-0.786715\pi$
$307$	−1.56298e8	+	1.31150e8i	−0.308297	+	0.258692i	0.475491	+	0.879721i	$0.342271\pi$
$308$	−3.30828e8	+	1.20412e8i	−0.645172	+	0.234823i
$309$	−5.08798e8	−	1.85187e8i	−0.981050	−	0.357073i
$310$	1.35628e8	+	1.13805e8i	0.258572	+	0.216968i
$311$	−3.14029e8	+	5.43914e8i	−0.591982	+	1.02534i	0.401983	+	0.915647i	$0.368321\pi$
$311$	−3.14029e8	+	5.43914e8i	−0.591982	+	1.02534i	−0.993965	+	0.109696i	$0.965012\pi$
$312$	−1.03947e8	−	1.80041e8i	−0.193762	−	0.335606i
$313$	−9.21716e7	+	5.22731e8i	−0.169899	+	0.963548i	0.773968	+	0.633224i	$0.218269\pi$
$313$	−9.21716e7	+	5.22731e8i	−0.169899	+	0.963548i	−0.943868	+	0.330323i	$0.892842\pi$
$314$	9.26869e7	−	5.25653e8i	0.168952	−	0.958177i
$315$	−4.03158e7	−	6.98290e7i	−0.0726755	−	0.125878i
$316$	−2.62588e7	+	4.54816e7i	−0.0468134	+	0.0810833i
$317$	−1.29194e8	−	1.08407e8i	−0.227790	−	0.191139i	0.521748	−	0.853100i	$-0.325280\pi$
$317$	−1.29194e8	−	1.08407e8i	−0.227790	−	0.191139i	−0.749538	+	0.661961i	$0.769725\pi$
$318$	4.35675e8	+	1.58573e8i	0.759745	+	0.276525i
$319$	−1.26036e8	+	4.58735e7i	−0.217384	+	0.0791215i
$320$	4.11223e7	−	3.45057e7i	0.0701541	−	0.0588663i
$321$	9.37079e7	+	5.31444e8i	0.158128	+	0.896788i
$322$	−1.41598e9			−2.36353
$323$	8.46746e8	+	6.92222e8i	1.39812	+	1.14297i
$324$	−3.36189e8			−0.549131
$325$	5.17800e7	+	2.93659e8i	0.0836701	+	0.474517i
$326$	6.07010e7	−	5.09342e7i	0.0970363	−	0.0814231i
$327$	4.33388e8	−	1.57741e8i	0.685425	−	0.249474i
$328$	−3.30936e6	−	1.20451e6i	−0.00517829	−	0.00188474i
$329$	8.91568e8	+	7.48114e8i	1.38028	+	1.15820i
$330$	1.36241e8	−	2.35977e8i	0.208694	−	0.361468i
$331$	2.43579e8	+	4.21891e8i	0.369183	+	0.639443i	0.989438	−	0.144957i	$-0.0463043\pi$
$331$	2.43579e8	+	4.21891e8i	0.369183	+	0.639443i	−0.620255	+	0.784400i	$0.712971\pi$
$332$	−1.18251e7	+	6.70637e7i	−0.0177347	+	0.100578i
$333$	−1.71427e7	+	9.72208e7i	−0.0254404	+	0.144279i
$334$	−3.40326e7	−	5.89461e7i	−0.0499784	−	0.0865651i
$335$	2.27221e8	−	3.93559e8i	0.330212	−	0.571943i
$336$	2.52023e8	+	2.11472e8i	0.362454	+	0.304135i
$337$	−8.31377e8	−	3.02597e8i	−1.18330	−	0.430685i	−0.325931	−	0.945394i	$-0.605678\pi$
$337$	−8.31377e8	−	3.02597e8i	−1.18330	−	0.430685i	−0.857365	+	0.514709i	$0.827900\pi$
$338$	3.86290e7	−	1.40598e7i	0.0544133	−	0.0198048i
$339$	3.70005e8	−	3.10471e8i	0.515833	−	0.432835i
$340$	8.32510e7	+	4.72140e8i	0.114872	+	0.651470i
$341$	−3.64760e8			−0.498158
$342$	−4.37850e7	+	3.77059e7i	−0.0591880	+	0.0509704i
$343$	1.64509e9			2.20120
$344$	−9.06868e6	−	5.14311e7i	−0.0120113	−	0.0681194i
$345$	8.39522e8	−	7.04442e8i	1.10069	−	0.923589i
$346$	1.52568e7	−	5.55303e6i	0.0198015	−	0.00720715i
$347$	3.61749e7	+	1.31666e7i	0.0464787	+	0.0169169i	0.365155	−	0.930947i	$-0.381016\pi$
$347$	3.61749e7	+	1.31666e7i	0.0464787	+	0.0169169i	−0.318676	+	0.947864i	$0.603238\pi$
$348$	9.60137e7	+	8.05651e7i	0.122125	+	0.102475i
$349$	1.37156e8	−	2.37561e8i	0.172713	−	0.299148i	−0.766654	−	0.642060i	$-0.778080\pi$
$349$	1.37156e8	−	2.37561e8i	0.172713	−	0.299148i	0.939368	+	0.342912i	$0.111413\pi$
$350$	−2.35943e8	−	4.08666e8i	−0.294151	−	0.509484i
$351$	1.37168e8	−	7.77918e8i	0.169308	−	0.960193i
$352$	−1.92047e7	+	1.08915e8i	−0.0234697	+	0.133104i
$353$	−4.70137e7	−	8.14300e7i	−0.0568869	−	0.0985311i	0.836180	−	0.548456i	$-0.184784\pi$
$353$	−4.70137e7	−	8.14300e7i	−0.0568869	−	0.0985311i	−0.893066	+	0.449925i	$0.851451\pi$
$354$	2.16736e8	−	3.75398e8i	0.259669	−	0.449760i
$355$	6.93076e8	+	5.81559e8i	0.822207	+	0.689914i
$356$	−4.43333e8	−	1.61360e8i	−0.520781	−	0.189549i
$357$	−2.76101e9	+	1.00492e9i	−3.21165	+	1.16895i
$358$	3.21172e8	−	2.69496e8i	0.369954	−	0.310428i
$359$	1.90511e8	+	1.08044e9i	0.217315	+	1.23245i	0.876844	+	0.480775i	$0.159645\pi$
$359$	1.90511e8	+	1.08044e9i	0.217315	+	1.23245i	−0.659529	+	0.751679i	$0.729244\pi$
$360$	−2.53294e7			−0.0286132
$361$	1.32624e8	−	8.83978e8i	0.148371	−	0.988932i
$362$	−8.43349e8			−0.934388
$363$	−6.92800e7	−	3.92907e8i	−0.0760212	−	0.431138i
$364$	−6.58380e8	+	5.52447e8i	−0.715520	+	0.600393i
$365$	8.24426e7	−	3.00067e7i	0.0887415	−	0.0322993i
$366$	−6.53376e8	−	2.37809e8i	−0.696593	−	0.253539i
$367$	−7.21252e8	−	6.05202e8i	−0.761651	−	0.639101i	0.176905	−	0.984228i	$-0.443391\pi$
$367$	−7.21252e8	−	6.05202e8i	−0.761651	−	0.639101i	−0.938556	+	0.345127i	$0.887836\pi$
$368$	−2.22406e8	+	3.85219e8i	−0.232638	+	0.402940i
$369$	830865.	+	1.43910e6i	0.000860871	+	0.00149107i
$370$	1.16247e8	−	6.59267e8i	0.119309	−	0.676637i
$371$	3.32836e8	−	1.88760e9i	0.338393	−	1.91912i
$372$	1.70430e8	+	2.95194e8i	0.171651	+	0.297308i
$373$	−3.61781e8	+	6.26624e8i	−0.360965	+	0.625210i	−0.988120	−	0.153685i	$-0.950886\pi$
$373$	−3.61781e8	+	6.26624e8i	−0.360965	+	0.625210i	0.627155	+	0.778895i	$0.284219\pi$
$374$	−7.56635e8	−	6.34893e8i	−0.747887	−	0.627552i
$375$	1.08406e9	+	3.94565e8i	1.06156	+	0.386375i
$376$	3.43563e8	−	1.25047e8i	0.333311	−	0.121315i
$377$	−2.50824e8	+	2.10467e8i	−0.241088	+	0.202297i
$378$	2.17069e8	+	1.23106e9i	0.206717	+	1.17235i
$379$	−1.35506e9			−1.27856			−0.639282	−	0.768972i	$-0.720768\pi$
$379$	−1.35506e9			−1.27856			−0.639282	+	0.768972i	$0.720768\pi$
$380$	2.96912e8	−	2.55689e8i	0.277578	−	0.239039i
$381$	2.12979e9			1.97287
$382$	1.14615e8	+	6.50016e8i	0.105201	+	0.596627i
$383$	1.04037e9	−	8.72977e8i	0.946223	−	0.793975i	−0.0324348	−	0.999474i	$-0.510326\pi$
$383$	1.04037e9	−	8.72977e8i	0.946223	−	0.793975i	0.978657	+	0.205499i	$0.0658817\pi$
$384$	9.71164e7	−	3.53475e7i	0.0875252	−	0.0318566i
$385$	−1.05854e9	−	3.85277e8i	−0.945353	−	0.344080i
$386$	−3.85944e7	−	3.23845e7i	−0.0341561	−	0.0286604i
$387$	−1.23210e7	+	2.13406e7i	−0.0108058	+	0.0187162i
$388$	−1.16999e8	−	2.02649e8i	−0.101688	−	0.176130i
$389$	−1.50865e8	+	8.55600e8i	−0.129947	+	0.736965i	0.848299	+	0.529517i	$0.177627\pi$
$389$	−1.50865e8	+	8.55600e8i	−0.129947	+	0.736965i	−0.978246	+	0.207448i	$0.933484\pi$
$390$	1.15509e8	−	6.55082e8i	0.0986026	−	0.559203i
$391$	−1.98629e9	−	3.44035e9i	−1.68044	−	2.91061i
$392$	4.69220e8	−	8.12712e8i	0.393437	−	0.681453i
$393$	6.09683e8	+	5.11585e8i	0.506676	+	0.425151i
$394$	−3.73644e8	−	1.35995e8i	−0.307767	−	0.112018i
$395$	−1.57905e8	+	5.74726e7i	−0.128916	+	0.0469214i
$396$	3.99754e7	−	3.35434e7i	0.0323489	−	0.0271440i
$397$	1.57991e8	+	8.96011e8i	0.126726	+	0.718698i	0.980268	+	0.197674i	$0.0633388\pi$
$397$	1.57991e8	+	8.96011e8i	0.126726	+	0.718698i	−0.853542	+	0.521024i	$0.825550\pi$
$398$	1.31754e9			1.04755
$399$	1.85919e9	+	1.51990e9i	1.46527	+	1.19787i
$400$	−1.48238e8			−0.115811
$401$	−2.67726e7	−	1.51835e8i	−0.0207341	−	0.117589i	0.972684	−	0.232133i	$-0.0745704\pi$
$401$	−2.67726e7	−	1.51835e8i	−0.0207341	−	0.117589i	−0.993418	+	0.114544i	$0.963459\pi$
$402$	6.70218e8	−	5.62379e8i	0.514546	−	0.431756i
$403$	−8.36757e8	+	3.04555e8i	−0.636842	+	0.231792i
$404$	5.09496e8	+	1.85441e8i	0.384420	+	0.139918i
$405$	−8.24027e8	−	6.91441e8i	−0.616381	−	0.517205i
$406$	2.59079e8	−	4.48738e8i	0.192128	−	0.332776i
$407$	6.89594e8	+	1.19441e9i	0.507006	+	0.878160i
$408$	−1.60277e8	+	9.08978e8i	−0.116832	+	0.662587i
$409$	4.79913e8	−	2.72172e9i	0.346841	−	1.96704i	0.123029	−	0.992403i	$-0.460739\pi$
$409$	4.79913e8	−	2.72172e9i	0.346841	−	1.96704i	0.223813	−	0.974632i	$-0.428150\pi$
$410$	−5.63421e6	−	9.75873e6i	−0.00403728	−	0.00699278i
$411$	1.11287e8	−	1.92754e8i	0.0790672	−	0.136948i
$412$	5.38663e8	+	4.51992e8i	0.379469	+	0.318413i
$413$	−1.68395e9	−	6.12908e8i	−1.17626	−	0.428125i
$414$	1.97226e8	−	7.17845e7i	0.136604	−	0.0497198i
$415$	−1.66914e8	+	1.40058e8i	−0.114637	+	0.0961920i
$416$	4.68828e7	+	2.65886e8i	0.0319291	+	0.181079i
$417$	−7.58489e8			−0.512239
$418$	−1.29988e8	+	7.96729e8i	−0.0870533	+	0.533573i
$419$	−1.26974e9			−0.843270			−0.421635	−	0.906766i	$-0.638544\pi$
$419$	−1.26974e9			−0.843270			−0.421635	+	0.906766i	$0.638544\pi$
$420$	1.82793e8	+	1.03667e9i	0.120389	+	0.682762i
$421$	1.11569e9	−	9.36176e8i	0.728713	−	0.611463i	−0.201067	−	0.979577i	$-0.564441\pi$
$421$	1.11569e9	−	9.36176e8i	0.728713	−	0.611463i	0.929780	+	0.368114i	$0.119997\pi$
$422$	3.87727e8	−	1.41121e8i	0.251149	−	0.0914109i
$423$	−1.62110e8	−	5.90030e7i	−0.104140	−	0.0379038i
$424$	−4.61248e8	−	3.87033e8i	−0.293869	−	0.246585i
$425$	6.61948e8	−	1.14653e9i	0.418276	−	0.724475i
$426$	8.70922e8	+	1.50848e9i	0.545815	+	0.945380i
$427$	−4.99149e8	+	2.83081e9i	−0.310265	+	1.75960i
$428$	1.21697e8	−	6.90178e8i	0.0750285	−	0.425508i
$429$	6.85216e8	+	1.18683e9i	0.419013	+	0.725751i
$430$	8.35503e7	−	1.44713e8i	0.0506767	−	0.0877746i
$431$	1.79906e9	+	1.50959e9i	1.08237	+	0.908216i	0.996115	−	0.0880573i	$-0.0280659\pi$
$431$	1.79906e9	+	1.50959e9i	1.08237	+	0.908216i	0.0862541	+	0.996273i	$0.472510\pi$
$432$	3.69007e8	+	1.34308e8i	0.220212	+	0.0801507i
$433$	1.01157e9	−	3.68180e8i	0.598806	−	0.217948i	−0.0247921	−	0.999693i	$-0.507892\pi$
$433$	1.01157e9	−	3.68180e8i	0.598806	−	0.217948i	0.623598	+	0.781745i	$0.285670\pi$
$434$	1.07948e9	−	9.05789e8i	0.633869	−	0.531879i
$435$	6.96392e7	+	3.94943e8i	0.0405640	+	0.230050i
$436$	−5.98956e8			−0.346092
$437$	−1.58726e9	+	2.83236e9i	−0.909834	+	1.62354i
$438$	1.68907e8			0.0960482
$439$	4.87461e8	+	2.76453e9i	0.274988	+	1.55954i	0.738999	+	0.673707i	$0.235299\pi$
$439$	4.87461e8	+	2.76453e9i	0.274988	+	1.55954i	−0.464011	+	0.885830i	$0.653590\pi$
$440$	−2.71079e8	+	2.27462e8i	−0.151709	+	0.127299i
$441$	−4.16096e8	+	1.51447e8i	−0.231025	+	0.0840862i
$442$	−2.26582e9	−	8.24689e8i	−1.24809	−	0.454268i
$443$	−1.57873e9	−	1.32471e9i	−0.862771	−	0.723951i	0.0997922	−	0.995008i	$-0.468182\pi$
$443$	−1.57873e9	−	1.32471e9i	−0.862771	−	0.723951i	−0.962563	+	0.271058i	$0.912627\pi$
$444$	6.44411e8	−	1.11615e9i	0.349400	−	0.605178i
$445$	−7.54777e8	−	1.30731e9i	−0.406030	−	0.703265i
$446$	−6.08428e7	+	3.45057e8i	−0.0324741	+	0.184170i
$447$	−6.58604e6	+	3.73513e7i	−0.00348777	+	0.0197801i
$448$	−2.13629e8	−	3.70016e8i	−0.112250	−	0.194423i
$449$	−1.14718e8	+	1.98697e8i	−0.0598092	+	0.103593i	−0.894380	−	0.447309i	$-0.852383\pi$
$449$	−1.14718e8	+	1.98697e8i	−0.0598092	+	0.103593i	0.834570	+	0.550901i	$0.185716\pi$
$450$	5.35814e7	+	4.49602e7i	0.0277185	+	0.0232586i
$451$	2.18153e7	+	7.94014e6i	0.0111981	+	0.00407577i
$452$	−5.89444e8	+	2.14540e8i	−0.300233	+	0.109276i
$453$	−2.45027e9	+	2.05602e9i	−1.23842	+	1.03916i
$454$	4.14442e8	+	2.35042e9i	0.207859	+	1.17883i
$455$	−2.74996e9			−1.36863
$456$	7.05514e8	−	2.67066e8i	0.348440	−	0.131899i
$457$	1.04177e9			0.510582			0.255291	−	0.966864i	$-0.417829\pi$
$457$	1.04177e9			0.510582			0.255291	+	0.966864i	$0.417829\pi$
$458$	−3.06057e8	−	1.73574e9i	−0.148859	−	0.844219i
$459$	−2.68657e9	+	2.25430e9i	−1.29674	+	1.08810i
$460$	−1.33742e9	+	4.86780e8i	−0.640641	+	0.233174i
$461$	3.91825e9	+	1.42613e9i	1.86268	+	0.677962i	0.976837	+	0.213986i	$0.0686446\pi$
$461$	3.91825e9	+	1.42613e9i	1.86268	+	0.677962i	0.885848	+	0.463976i	$0.153578\pi$
$462$	−1.66134e9	−	1.39403e9i	−0.783810	−	0.657694i
$463$	1.20275e9	−	2.08323e9i	0.563174	−	0.975446i	−0.434043	−	0.900892i	$-0.642913\pi$
$463$	1.20275e9	−	2.08323e9i	0.563174	−	0.975446i	0.997217	−	0.0745538i	$-0.0237533\pi$
$464$	−8.13865e7	−	1.40966e8i	−0.0378216	−	0.0655089i
$465$	−1.89387e8	+	1.07407e9i	−0.0873506	+	0.495390i
$466$	−2.85197e8	+	1.61743e9i	−0.130555	+	0.740415i
$467$	−2.53966e8	−	4.39882e8i	−0.115390	−	0.199861i	0.802546	−	0.596590i	$-0.203478\pi$
$467$	−2.53966e8	−	4.39882e8i	−0.115390	−	0.199861i	−0.917935	+	0.396730i	$0.870145\pi$
$468$	6.36964e7	−	1.10325e8i	0.0287246	−	0.0497525i
$469$	−2.77076e9	−	2.32494e9i	−1.24021	−	1.04066i
$470$	1.09929e9	+	4.00107e8i	0.488392	+	0.177760i
$471$	3.08973e9	−	1.12457e9i	1.36253	−	0.495922i
$472$	−4.31239e8	+	3.61853e8i	−0.188765	+	0.158393i
$473$	5.97808e7	+	3.39034e8i	0.0259745	+	0.147309i
$474$	−3.23513e8			−0.139530
$475$	−1.08193e9	+	1.38561e7i	−0.463205	+	0.00593218i
$476$	3.81579e9			1.62166
$477$	4.93347e7	+	2.79791e8i	0.0208132	+	0.118037i
$478$	3.21755e8	−	2.69984e8i	0.134750	−	0.113068i
$479$	−5.35316e8	+	1.94839e8i	−0.222554	+	0.0810031i	−0.450891	−	0.892579i	$-0.648894\pi$
$479$	−5.35316e8	+	1.94839e8i	−0.222554	+	0.0810031i	0.228337	+	0.973582i	$0.426671\pi$
$480$	3.10740e8	+	1.13100e8i	0.128248	+	0.0466786i
$481$	2.57919e9	+	2.16420e9i	1.05676	+	0.886726i
$482$	6.30892e7	−	1.09274e8i	0.0256620	−	0.0444479i
$483$	−4.36127e9	−	7.55395e9i	−1.76116	−	3.05042i
$484$	−8.99728e7	+	5.10261e8i	−0.0360705	+	0.204566i
$485$	1.30013e8	−	7.37341e8i	0.0517477	−	0.293476i
$486$	−1.96794e8	−	3.40858e8i	−0.0777652	−	0.134693i
$487$	−1.49976e9	+	2.59766e9i	−0.588396	+	1.01913i	0.406047	+	0.913852i	$0.366907\pi$
$487$	−1.49976e9	+	2.59766e9i	−0.588396	+	1.01913i	−0.994443	+	0.105279i	$0.966426\pi$
$488$	6.91726e8	+	5.80427e8i	0.269442	+	0.226089i
$489$	4.58685e8	+	1.66948e8i	0.177392	+	0.0645653i
$490$	2.82160e9	−	1.02698e9i	1.08345	−	0.394344i
$491$	2.80282e9	−	2.35185e9i	1.06859	−	0.896652i	0.0736642	−	0.997283i	$-0.476531\pi$
$491$	2.80282e9	−	2.35185e9i	1.06859	−	0.896652i	0.994924	+	0.100631i	$0.0320862\pi$
$492$	−3.76717e6	−	2.13647e7i	−0.00142606	−	0.00808759i
$493$	1.45371e9			0.546404
$494$	3.67034e8	+	1.93622e9i	0.136981	+	0.722621i
$495$	1.66972e8			0.0618764
$496$	−7.68689e7	−	4.35945e8i	−0.0282855	−	0.160415i
$497$	5.51628e9	−	4.62871e9i	2.01557	−	1.69127i
$498$	−3.94193e8	+	1.43474e8i	−0.143023	+	0.0520561i
$499$	−4.07349e9	−	1.48263e9i	−1.46762	−	0.534171i	−0.520169	−	0.854063i	$-0.674131\pi$
$499$	−4.07349e9	−	1.48263e9i	−1.46762	−	0.534171i	−0.947454	+	0.319892i	$0.896353\pi$
$500$	−1.14769e9	−	9.63026e8i	−0.410610	−	0.344543i
$501$	2.09643e8	−	3.63113e8i	0.0744817	−	0.129006i
$502$	9.60170e8	+	1.66306e9i	0.338755	+	0.586740i
$503$	−1.07396e8	+	6.09076e8i	−0.0376272	+	0.213395i	−0.997824	−	0.0659287i	$-0.978999\pi$
$503$	−1.07396e8	+	6.09076e8i	−0.0376272	+	0.213395i	0.960197	+	0.279323i	$0.0901101\pi$
$504$	−3.50075e7	+	1.98538e8i	−0.0121802	+	0.0690774i
$505$	8.67419e8	+	1.50241e9i	0.299716	+	0.519123i
$506$	1.46610e9	−	2.53937e9i	0.503081	−	0.871362i
$507$	1.93985e8	+	1.62773e8i	0.0661060	+	0.0554695i
$508$	−2.59912e9	−	9.46001e8i	−0.879636	−	0.320161i
$509$	−3.17457e9	+	1.15545e9i	−1.06702	+	0.388363i	−0.815061	−	0.579375i	$-0.803297\pi$
$509$	−3.17457e9	+	1.15545e9i	−1.06702	+	0.388363i	−0.251958	+	0.967738i	$0.581074\pi$
$510$	−2.26235e9	+	1.89834e9i	−0.755204	+	0.633691i
$511$	−1.21256e8	−	6.87675e8i	−0.0402002	−	0.227987i
$512$	−1.34218e8			−0.0441942
$513$	2.70580e9	+	9.45771e8i	0.884882	+	0.309297i
$514$	1.36506e9			0.443386
$515$	3.90694e8	+	2.21574e9i	0.126041	+	0.714814i
$516$	2.46442e8	−	2.06789e8i	0.0789661	−	0.0662604i
$517$	−2.26477e9	+	8.24309e8i	−0.720788	+	0.262345i
$518$	−5.00681e9	−	1.82233e9i	−1.58273	−	0.576067i
$519$	7.66159e7	+	6.42883e7i	0.0240565	+	0.0201858i
$520$	−4.31934e8	+	7.48132e8i	−0.134712	+	0.233328i
$521$	−6.87393e8	−	1.19060e9i	−0.212948	−	0.368836i	0.739688	−	0.672950i	$-0.234973\pi$
$521$	−6.87393e8	−	1.19060e9i	−0.212948	−	0.368836i	−0.952636	+	0.304114i	$0.901640\pi$
$522$	−1.33369e7	+	7.56372e7i	−0.00410400	+	0.0232750i
$523$	−3.10579e8	+	1.76138e9i	−0.0949326	+	0.538390i	0.899835	+	0.436230i	$0.143686\pi$
$523$	−3.10579e8	+	1.76138e9i	−0.0949326	+	0.538390i	−0.994768	+	0.102160i	$0.967425\pi$
$524$	−5.16801e8	−	8.95125e8i	−0.156915	−	0.271784i
$525$	1.45343e9	−	2.51742e9i	0.438366	−	0.759273i
$526$	3.36416e9	+	2.82287e9i	1.00792	+	0.845747i
$527$	3.71502e9	+	1.35216e9i	1.10567	+	0.402430i
$528$	−6.40192e8	+	2.33011e8i	−0.189274	+	0.0688902i
$529$	6.42592e9	−	5.39199e9i	1.88730	−	1.58363i
$530$	−3.34545e8	−	1.89730e9i	−0.0976088	−	0.553567i
$531$	2.65623e8			0.0769902
$532$	−1.59378e9	−	2.68064e9i	−0.458922	−	0.771877i
$533$	5.66738e7			0.0162120
$534$	−5.04663e8	−	2.86209e9i	−0.143419	−	0.813370i
$535$	1.71778e9	−	1.44139e9i	0.484986	−	0.406951i
$536$	−1.06770e9	+	3.88612e8i	−0.299484	+	0.109003i
$537$	2.42693e9	+	8.83329e8i	0.676312	+	0.246157i
$538$	7.44200e8	+	6.24458e8i	0.206040	+	0.172888i
$539$	−3.09310e9	+	5.35740e9i	−0.850811	+	1.47365i
$540$	6.28236e8	+	1.08814e9i	0.171690	+	0.297376i
$541$	−5.86879e8	+	3.32836e9i	−0.159352	+	0.903731i	0.795346	+	0.606156i	$0.207289\pi$
$541$	−5.86879e8	+	3.32836e9i	−0.159352	+	0.903731i	−0.954698	+	0.297576i	$0.903822\pi$
$542$	−1.73606e8	+	9.84570e8i	−0.0468347	+	0.265613i
$543$	−2.59755e9	−	4.49909e9i	−0.696249	−	1.20594i
$544$	5.99343e8	−	1.03809e9i	0.159617	−	0.276465i
$545$	−1.46809e9	−	1.23187e9i	−0.388477	−	0.325971i
$546$	−4.97503e9	−	1.81076e9i	−1.30804	−	0.476088i
$547$	2.37225e9	−	8.63428e8i	0.619733	−	0.225564i	−0.0130236	−	0.999915i	$-0.504146\pi$
$547$	2.37225e9	−	8.63428e8i	0.619733	−	0.225564i	0.632756	+	0.774351i	$0.281923\pi$
$548$	−2.21427e8	+	1.85799e8i	−0.0574775	+	0.0482293i
$549$	−7.39865e7	−	4.19598e8i	−0.0190831	−	0.108226i
$550$	9.77183e8			0.250442
$551$	−6.07187e8	−	1.02125e9i	−0.154629	−	0.260077i
$552$	−2.74008e9			−0.693389
$553$	2.32244e8	+	1.31712e9i	0.0583992	+	0.331198i
$554$	−3.69038e9	+	3.09659e9i	−0.922118	+	0.773749i
$555$	3.87510e9	−	1.41042e9i	0.962182	−	0.350206i
$556$	9.25632e8	+	3.36902e8i	0.228390	+	0.0831271i
$557$	4.25125e9	+	3.56722e9i	1.04237	+	0.874656i	0.992271	−	0.124088i	$-0.0396006\pi$
$557$	4.25125e9	+	3.56722e9i	1.04237	+	0.874656i	0.0501029	+	0.998744i	$0.484045\pi$
$558$	−1.04436e8	+	1.80889e8i	−0.0254467	+	0.0440751i
$559$	4.20211e8	+	7.27827e8i	0.101748	+	0.176233i
$560$	2.37391e8	−	1.34631e9i	0.0571223	−	0.323957i
$561$	1.05655e9	−	5.99199e9i	0.252650	−	1.43285i
$562$	6.13202e7	+	1.06210e8i	0.0145723	+	0.0252399i
$563$	−7.25228e8	+	1.25613e9i	−0.171276	+	0.296658i	−0.938866	−	0.344283i	$-0.888122\pi$
$563$	−7.25228e8	+	1.25613e9i	−0.171276	+	0.296658i	0.767591	+	0.640941i	$0.221456\pi$
$564$	1.72529e9	+	1.44769e9i	0.404934	+	0.339780i
$565$	−1.88602e9	−	6.86456e8i	−0.439924	−	0.160119i
$566$	−4.17381e9	+	1.51914e9i	−0.967553	+	0.352160i
$567$	−6.55854e9	+	5.50327e9i	−1.51101	+	1.26788i
$568$	−3.92810e8	−	2.22774e9i	−0.0899422	−	0.510088i
$569$	−7.25764e9			−1.65159			−0.825795	−	0.563970i	$-0.809273\pi$
$569$	−7.25764e9			−1.65159			−0.825795	+	0.563970i	$0.809273\pi$
$570$	2.27855e9	+	7.96430e8i	0.515343	+	0.180130i
$571$	−1.38187e8			−0.0310629			−0.0155314	−	0.999879i	$-0.504944\pi$
$571$	−1.38187e8			−0.0310629			−0.0155314	+	0.999879i	$0.504944\pi$
$572$	−3.09052e8	−	1.75272e9i	−0.0690470	−	0.391585i
$573$	−3.11468e9	+	2.61353e9i	−0.691628	+	0.580345i
$574$	−8.42779e7	+	3.06747e7i	−0.0186004	+	0.00676999i
$575$	3.69319e9	+	1.34421e9i	0.810148	+	0.294870i
$576$	4.85138e7	+	4.07079e7i	0.0105776	+	0.00887566i
$577$	8.29005e8	−	1.43588e9i	0.179656	−	0.311173i	−0.762107	−	0.647451i	$-0.775835\pi$
$577$	8.29005e8	−	1.43588e9i	0.179656	−	0.311173i	0.941763	+	0.336278i	$0.109168\pi$
$578$	3.71132e9	+	6.42819e9i	0.799430	+	1.38465i
$579$	5.38923e7	−	3.05638e8i	0.0115386	−	0.0654385i
$580$	9.04392e7	−	5.12906e8i	0.0192468	−	0.109154i
$581$	8.67112e8	+	1.50188e9i	0.183425	+	0.317702i
$582$	7.20725e8	−	1.24833e9i	0.151544	−	0.262482i
$583$	3.04055e9	+	2.55132e9i	0.635494	+	0.533243i
$584$	−2.06128e8	−	7.50246e7i	−0.0428246	−	0.0155869i
$585$	3.83032e8	−	1.39412e8i	0.0791024	−	0.0287909i
$586$	−7.25216e8	+	6.08528e8i	−0.148876	+	0.124922i
$587$	−4.40006e7	−	2.49540e8i	−0.00897893	−	0.0509221i	0.979989	−	0.199051i	$-0.0637860\pi$
$587$	−4.40006e7	−	2.49540e8i	−0.00897893	−	0.0509221i	−0.988968	+	0.148129i	$0.952675\pi$
$588$	5.78087e9			1.17266
$589$	−6.01787e8	−	3.17462e9i	−0.121350	−	0.640160i
$590$	−1.80123e9			−0.361066
$591$	−4.25333e8	−	2.41219e9i	−0.0847565	−	0.480678i
$592$	−1.28218e9	+	1.07588e9i	−0.253994	+	0.213127i
$593$	−5.25830e9	+	1.91386e9i	−1.03551	+	0.376894i	−0.803176	−	0.595742i	$-0.796858\pi$
$593$	−5.25830e9	+	1.91386e9i	−1.03551	+	0.376894i	−0.232333	+	0.972636i	$0.574636\pi$
$594$	−2.43250e9	−	8.85356e8i	−0.476211	−	0.173327i
$595$	9.35282e9	+	7.84795e9i	1.82026	+	1.52738i
$596$	2.46279e7	−	4.26568e7i	0.00476503	−	0.00825327i
$597$	4.05808e9	+	7.02880e9i	0.780568	+	1.35198i
$598$	1.24300e9	−	7.04940e9i	0.237693	−	1.34802i
$599$	2.22672e7	−	1.26284e8i	0.00423323	−	0.0240078i	−0.982618	−	0.185639i	$-0.940564\pi$
$599$	2.22672e7	−	1.26284e8i	0.00423323	−	0.0240078i	0.986851	+	0.161631i	$0.0516756\pi$
$600$	−4.56578e8	−	7.90817e8i	−0.0862951	−	0.149467i
$601$	−4.44003e8	+	7.69036e8i	−0.0834306	+	0.144506i	−0.904721	−	0.426004i	$-0.859921\pi$
$601$	−4.44003e8	+	7.69036e8i	−0.0834306	+	0.144506i	0.821291	+	0.570510i	$0.193254\pi$
$602$	−1.01882e9	−	8.54891e8i	−0.190331	−	0.159707i
$603$	5.03794e8	+	1.83366e8i	0.0935712	+	0.0340571i
$604$	3.90345e9	−	1.42074e9i	0.720807	−	0.262352i
$605$	−1.26999e9	+	1.06565e9i	−0.233161	+	0.195645i
$606$	5.79979e8	+	3.28922e9i	0.105866	+	0.600398i
$607$	−1.02550e10			−1.86112			−0.930561	−	0.366136i	$-0.880680\pi$
$607$	−1.02550e10			−1.86112			−0.930561	+	0.366136i	$0.880680\pi$
$608$	−9.79607e8	+	1.25457e7i	−0.176762	+	0.00226376i
$609$	3.19190e9			0.572649
$610$	5.01712e8	+	2.84535e9i	0.0894953	+	0.507553i
$611$	−4.50711e9	+	3.78192e9i	−0.799382	+	0.670761i
$612$	−5.31487e8	+	1.93445e8i	−0.0937266	+	0.0341137i
$613$	3.14608e9	+	1.14508e9i	0.551643	+	0.200782i	0.602777	−	0.797910i	$-0.294061\pi$
$613$	3.14608e9	+	1.14508e9i	0.551643	+	0.200782i	−0.0511331	+	0.998692i	$0.516283\pi$
$614$	1.25039e9	+	1.04920e9i	0.217999	+	0.182923i
$615$	3.47072e7	−	6.01146e7i	0.00601667	−	0.0104212i
$616$	1.40824e9	+	2.43914e9i	0.242742	+	0.420441i
$617$	1.78328e9	−	1.01135e10i	0.305648	−	1.73341i	−0.314792	−	0.949161i	$-0.601935\pi$
$617$	1.78328e9	−	1.01135e10i	0.305648	−	1.73341i	0.620440	−	0.784254i	$-0.286954\pi$
$618$	−7.52177e8	+	4.26581e9i	−0.128192	+	0.727012i
$619$	3.10410e9	+	5.37647e9i	0.526040	+	0.911128i	0.999540	+	0.0303344i	$0.00965721\pi$
$619$	3.10410e9	+	5.37647e9i	0.526040	+	0.911128i	−0.473500	+	0.880794i	$0.657009\pi$
$620$	7.08197e8	−	1.22663e9i	0.119339	−	0.206702i
$621$	−7.97554e9	−	6.69227e9i	−1.33641	−	1.12138i
$622$	4.72145e9	+	1.71847e9i	0.786700	+	0.286335i
$623$	−1.12901e10	+	4.10928e9i	−1.87065	+	0.680859i
$624$	−1.27404e9	+	1.06905e9i	−0.209912	+	0.176137i
$625$	−3.41450e8	−	1.93646e9i	−0.0559431	−	0.317269i
$626$	4.24636e9			0.691842
$627$	−4.65075e9	+	1.76050e9i	−0.753506	+	0.285233i
$628$	−4.27010e9			−0.687985
$629$	−2.59574e9	−	1.47212e10i	−0.415896	−	2.35866i
$630$	−4.94139e8	+	4.14632e8i	−0.0787331	+	0.0660649i
$631$	6.88024e9	−	2.50420e9i	1.09019	−	0.396795i	0.266496	−	0.963836i	$-0.414134\pi$
$631$	6.88024e9	−	2.50420e9i	1.09019	−	0.396795i	0.823690	+	0.567041i	$0.191912\pi$
$632$	3.94804e8	+	1.43697e8i	0.0622116	+	0.0226432i
$633$	1.94707e9	+	1.63378e9i	0.305118	+	0.256024i
$634$	−6.74604e8	+	1.16845e9i	−0.105132	+	0.182095i
$635$	−4.42501e9	−	7.66434e9i	−0.685814	−	1.18786i
$636$	6.44076e8	−	3.65274e9i	0.0992744	−	0.563013i
$637$	−2.62241e9	+	1.48724e10i	−0.401987	+	2.27978i
$638$	5.36500e8	+	9.29246e8i	0.0817895	+	0.141664i
$639$	−5.33684e8	+	9.24368e8i	−0.0809154	+	0.140150i
$640$	−3.28979e8	−	2.76046e8i	−0.0496064	−	0.0416247i
$641$	1.03686e10	+	3.77387e9i	1.55495	+	0.565957i	0.969573	−	0.244802i	$-0.0787228\pi$
$641$	1.03686e10	+	3.77387e9i	1.55495	+	0.565957i	0.585381	+	0.810759i	$0.300945\pi$
$642$	4.05678e9	−	1.47655e9i	0.605075	−	0.220229i
$643$	7.08740e9	−	5.94704e9i	1.05135	−	0.882190i	0.0581182	−	0.998310i	$-0.481490\pi$
$643$	7.08740e9	−	5.94704e9i	1.05135	−	0.882190i	0.993235	+	0.116119i	$0.0370455\pi$
$644$	1.96706e9	+	1.11557e10i	0.290213	+	1.64588i
$645$	1.02935e9			0.151045
$646$	4.27735e9	−	7.63268e9i	0.624254	−	1.11394i
$647$	−9.73349e9			−1.41287			−0.706437	−	0.707776i	$-0.749699\pi$
$647$	−9.73349e9			−1.41287			−0.706437	+	0.707776i	$0.749699\pi$
$648$	4.67029e8	+	2.64865e9i	0.0674266	+	0.382395i
$649$	2.84273e9	−	2.38534e9i	0.408206	−	0.342526i
$650$	2.24165e9	−	8.15894e8i	0.320163	−	0.116530i
$651$	8.15703e9	+	2.96892e9i	1.15877	+	0.421759i
$652$	−4.85608e8	−	4.07473e8i	−0.0686150	−	0.0575748i
$653$	8.72175e8	−	1.51065e9i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$653$	8.72175e8	−	1.51065e9i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$654$	−1.84481e9	−	3.19530e9i	−0.257887	−	0.446673i
$655$	5.74285e8	−	3.25693e9i	0.0798515	−	0.452860i
$656$	−4.89237e6	+	2.77460e7i	−0.000676637	+	0.00383740i
$657$	5.17516e7	+	8.96364e7i	0.00711943	+	0.0123312i
$658$	4.65544e9	−	8.06345e9i	0.637044	−	1.10339i
$659$	−4.89538e9	−	4.10771e9i	−0.666327	−	0.559115i	0.245649	−	0.969359i	$-0.420999\pi$
$659$	−4.89538e9	−	4.10771e9i	−0.666327	−	0.559115i	−0.911976	+	0.410244i	$0.865443\pi$
$660$	−2.04840e9	−	7.45555e8i	−0.277339	−	0.100943i
$661$	−1.49565e9	+	5.44372e8i	−0.201430	+	0.0733146i	−0.440765	−	0.897622i	$-0.645293\pi$
$661$	−1.49565e9	+	5.44372e8i	−0.201430	+	0.0733146i	0.239335	+	0.970937i	$0.423071\pi$
$662$	2.98547e9	−	2.50511e9i	0.399954	−	0.335602i
$663$	−2.57926e9	−	1.46277e10i	−0.343715	−	1.94930i
$664$	5.44786e8			0.0722167
$665$	1.60679e9	−	9.84842e9i	0.211876	−	1.29865i
$666$	7.89765e8			0.103595
$667$	7.49394e8	+	4.25002e9i	0.0977844	+	0.554563i
$668$	−4.17127e8	+	3.50011e8i	−0.0541441	+	0.0454323i
$669$	−2.02820e9	+	7.38206e8i	−0.261891	+	0.0953205i
$670$	−3.41629e9	−	1.24343e9i	−0.438827	−	0.159720i
$671$	−4.55986e9	−	3.82618e9i	−0.582671	−	0.488919i
$672$	1.31597e9	−	2.27933e9i	0.167284	−	0.289744i
$673$	−3.68404e8	−	6.38095e8i	−0.0465878	−	0.0806924i	0.841791	−	0.539803i	$-0.181501\pi$
$673$	−3.68404e8	−	6.38095e8i	−0.0465878	−	0.0806924i	−0.888379	+	0.459111i	$0.848168\pi$
$674$	−1.22906e9	+	6.97034e9i	−0.154619	+	0.876888i
$675$	6.02501e8	−	3.41695e9i	0.0754040	−	0.427637i
$676$	−1.64433e8	−	2.84806e8i	−0.0204727	−	0.0354597i
$677$	−3.89968e9	+	6.75444e9i	−0.483023	+	0.836621i	−0.999810	−	0.0194933i	$-0.993795\pi$
$677$	−3.89968e9	+	6.75444e9i	−0.483023	+	0.836621i	0.516787	+	0.856114i	$0.327128\pi$
$678$	−2.96004e9	−	2.48377e9i	−0.364749	−	0.306061i
$679$	−5.59974e9	−	2.03814e9i	−0.686474	−	0.249856i
$680$	3.60408e9	−	1.31178e9i	0.439556	−	0.159985i
$681$	−1.12625e10	+	9.45035e9i	−1.36653	+	1.14666i
$682$	5.06720e8	+	2.87375e9i	0.0611678	+	0.346900i
$683$	9.08936e9			1.09159			0.545797	−	0.837918i	$-0.316227\pi$
$683$	9.08936e9			1.09159			0.545797	+	0.837918i	$0.316227\pi$
$684$	3.57890e8	+	2.92578e8i	0.0427615	+	0.0349579i
$685$	−9.24868e8			−0.109942
$686$	−2.28534e9	−	1.29608e10i	−0.270281	−	1.53284i
$687$	8.31713e9	−	6.97890e9i	0.978644	−	0.821180i
$688$	−3.92600e8	+	1.42895e8i	−0.0459611	+	0.0167285i
$689$	9.10520e9	+	3.31402e9i	1.06053	+	0.386001i
$690$	−6.71617e9	−	5.63554e9i	−0.778305	−	0.653076i
$691$	−1.93189e9	+	3.34613e9i	−0.222746	+	0.385807i	−0.955641	−	0.294535i	$-0.904835\pi$
$691$	−1.93189e9	+	3.34613e9i	−0.222746	+	0.385807i	0.732895	+	0.680342i	$0.238169\pi$
$692$	−6.49438e7	−	1.12486e8i	−0.00745018	−	0.0129041i
$693$	2.30770e8	−	1.30876e9i	0.0263398	−	0.149380i
$694$	5.34788e7	−	3.03293e8i	0.00607328	−	0.0344433i
$695$	1.57589e9	+	2.72953e9i	0.178065	+	0.308418i
$696$	5.01348e8	−	8.68360e8i	0.0563647	−	0.0976265i
$697$	−1.92752e8	−	1.61738e8i	−0.0215617	−	0.0180924i
$698$	−2.06215e9	−	7.50561e8i	−0.229523	−	0.0835396i
$699$	−9.50708e9	+	3.46030e9i	−1.05288	+	0.383215i
$700$	−2.89189e9	+	2.42658e9i	−0.318668	+	0.267394i
$701$	−1.09277e9	−	6.19741e9i	−0.119816	−	0.679512i	−0.984252	−	0.176769i	$-0.943435\pi$
$701$	−1.09277e9	−	6.19741e9i	−0.119816	−	0.679512i	0.864436	−	0.502743i	$-0.167676\pi$
$702$	−6.31935e9			−0.689433
$703$	−9.25763e9	+	7.97231e9i	−1.00498	+	0.865447i
$704$	8.84764e8			0.0955703
$705$	1.25136e9	+	7.09681e9i	0.134499	+	0.762783i
$706$	−5.76233e8	+	4.83517e8i	−0.0616285	+	0.0517124i
$707$	1.29751e10	−	4.72255e9i	1.38084	−	0.502584i
$708$	−3.25865e9	−	1.18605e9i	−0.345081	−	0.125599i
$709$	−1.66319e9	−	1.39559e9i	−0.175259	−	0.147060i	0.550938	−	0.834546i	$-0.314270\pi$
$709$	−1.66319e9	−	1.39559e9i	−0.175259	−	0.147060i	−0.726198	+	0.687486i	$0.758714\pi$
$710$	3.61898e9	−	6.26826e9i	0.379474	−	0.657269i
$711$	−9.91213e7	−	1.71683e8i	−0.0103425	−	0.0179137i
$712$	−6.55397e8	+	3.71694e9i	−0.0680494	+	0.385928i
$713$	−2.03802e9	+	1.15582e10i	−0.210569	+	1.19420i
$714$	1.17528e10	+	2.03564e10i	1.20836	+	2.09295i
$715$	2.84731e9	−	4.93169e9i	0.291316	−	0.504573i
$716$	−2.56938e9	−	2.15597e9i	−0.261597	−	0.219506i
$717$	2.43133e9	+	8.84931e8i	0.246335	+	0.0896587i
$718$	8.24756e9	−	3.00187e9i	0.831553	−	0.302661i
$719$	−9.44072e9	+	7.92171e9i	−0.947227	+	0.794818i	−0.978828	−	0.204683i	$-0.934384\pi$
$719$	−9.44072e9	+	7.92171e9i	−0.947227	+	0.794818i	0.0316012	+	0.999501i	$0.489939\pi$
$720$	3.51873e7	+	1.99557e8i	0.00351336	+	0.0199252i
$721$	1.79074e10			1.77934
$722$	−7.14863e9	+	1.83133e8i	−0.706875	+	0.0181086i
$723$	7.77270e8			0.0764871
$724$	1.17157e9	+	6.64429e9i	0.114731	+	0.650674i
$725$	−1.10173e9	+	9.24461e8i	−0.107372	+	0.0900960i
$726$	−2.99926e9	+	1.09164e9i	−0.290895	+	0.105877i
$727$	2.64781e9	+	9.63726e8i	0.255574	+	0.0930214i	0.466630	−	0.884453i	$-0.345468\pi$
$727$	2.64781e9	+	9.63726e8i	0.255574	+	0.0930214i	−0.211056	+	0.977474i	$0.567690\pi$
$728$	5.26704e9	+	4.41957e9i	0.505949	+	0.424542i
$729$	−4.53184e9	+	7.84937e9i	−0.433239	+	0.750392i
$730$	−3.50934e8	−	6.07836e8i	−0.0333884	−	0.0578305i
$731$	6.47932e8	−	3.67461e9i	0.0613506	−	0.347936i
$732$	−9.65912e8	+	5.47796e9i	−0.0910225	+	0.516214i
$733$	−1.07649e9	−	1.86453e9i	−0.100959	−	0.174866i	0.811121	−	0.584878i	$-0.198858\pi$
$733$	−1.07649e9	−	1.86453e9i	−0.100959	−	0.174866i	−0.912080	+	0.410012i	$0.865524\pi$
$734$	−3.76611e9	+	6.52309e9i	−0.351525	+	0.608860i
$735$	1.41694e10	+	1.18895e10i	1.31627	+	1.10448i
$736$	3.34390e9	+	1.21708e9i	0.309158	+	0.112524i
$737$	7.03831e9	−	2.56174e9i	0.647638	−	0.235721i
$738$	1.01837e7	−	8.54512e6i	0.000932625	−	0.000782565i
$739$	−3.02696e9	−	1.71667e10i	−0.275899	−	1.56470i	−0.736091	−	0.676883i	$-0.763330\pi$
$739$	−3.02696e9	−	1.71667e10i	−0.275899	−	1.56470i	0.460192	−	0.887820i	$-0.347781\pi$
$740$	−5.35550e9			−0.485835
$741$	−9.19886e9	+	7.92169e9i	−0.830558	+	0.715244i
$742$	−1.53338e10			−1.37796
$743$	1.23987e9	+	7.03164e9i	0.110896	+	0.628920i	0.988701	+	0.149902i	$0.0478959\pi$
$743$	1.23987e9	+	7.03164e9i	0.110896	+	0.628920i	−0.877805	+	0.479018i	$0.840993\pi$
$744$	2.08892e9	−	1.75281e9i	0.185958	−	0.156038i
$745$	1.48097e8	−	5.39030e7i	0.0131220	−	0.00477602i
$746$	5.43941e9	+	1.97978e9i	0.479696	+	0.174595i
$747$	−1.96916e8	−	1.65232e8i	−0.0172846	−	0.0145035i
$748$	−3.95087e9	+	6.84311e9i	−0.345173	+	0.597858i
$749$	−8.92378e9	−	1.54564e10i	−0.776001	−	1.34407i
$750$	1.60261e9	−	9.08884e9i	0.138712	−	0.786673i
$751$	1.76129e9	−	9.98876e9i	0.151737	−	0.860541i	−0.809972	−	0.586468i	$-0.800518\pi$
$751$	1.76129e9	−	9.98876e9i	0.151737	−	0.860541i	0.961709	−	0.274073i	$-0.0883710\pi$
$752$	−1.46245e9	−	2.53304e9i	−0.125406	−	0.217210i
$753$	−5.91473e9	+	1.02446e10i	−0.504839	+	0.874406i
$754$	2.00660e9	+	1.68373e9i	0.170475	+	0.143045i
$755$	1.24897e10	+	4.54588e9i	1.05618	+	0.384418i
$756$	9.39732e9	−	3.42034e9i	0.791002	−	0.287901i
$757$	−7.44294e9	+	6.24536e9i	−0.623604	+	0.523266i	−0.898934	−	0.438084i	$-0.855657\pi$
$757$	−7.44294e9	+	6.24536e9i	−0.623604	+	0.523266i	0.275330	+	0.961350i	$0.411213\pi$
$758$	1.88243e9	+	1.06758e10i	0.156992	+	0.890346i
$759$	1.80626e10			1.49946
$760$	−2.42690e9	−	1.98401e9i	−0.200542	−	0.163944i
$761$	7.27784e9			0.598627			0.299313	−	0.954155i	$-0.403242\pi$
$761$	7.27784e9			0.598627			0.299313	+	0.954155i	$0.403242\pi$
$762$	−2.95867e9	−	1.67795e10i	−0.242245	−	1.37384i
$763$	−1.16847e10	+	9.80464e9i	−0.952319	+	0.799090i
$764$	4.96191e9	−	1.80599e9i	0.402552	−	0.146517i
$765$	−1.70058e9	−	6.18960e8i	−0.137335	−	0.0499859i
$766$	−8.32298e9	−	6.98381e9i	−0.669080	−	0.561425i
$767$	4.52958e9	−	7.84546e9i	0.362472	−	0.627820i
$768$	−4.13396e8	−	7.16023e8i	−0.0329308	−	0.0570378i
$769$	3.00230e9	−	1.70269e10i	0.238074	−	1.35018i	−0.597969	−	0.801519i	$-0.704026\pi$
$769$	3.00230e9	−	1.70269e10i	0.238074	−	1.35018i	0.836043	−	0.548664i	$-0.184863\pi$
$770$	−1.56488e9	+	8.87488e9i	−0.123527	+	0.700559i
$771$	4.20445e9	+	7.28232e9i	0.330384	+	0.572242i
$772$	−2.01525e8	+	3.49052e8i	−0.0157641	+	0.0273042i
$773$	6.04259e9	+	5.07034e9i	0.470538	+	0.394829i	0.846991	−	0.531607i	$-0.178412\pi$
$773$	6.04259e9	+	5.07034e9i	0.470538	+	0.394829i	−0.376453	+	0.926436i	$0.622856\pi$
$774$	1.85247e8	+	6.74244e7i	0.0143601	+	0.00522666i
$775$	−3.67540e9	+	1.33774e9i	−0.283628	+	0.103232i
$776$	−1.43403e9	+	1.20329e9i	−0.110164	+	0.0924388i
$777$	−5.69944e9	−	3.23232e10i	−0.435872	−	2.47195i
$778$	6.95039e9			0.529152
$779$	−3.31141e7	+	2.02965e8i	−0.00250976	+	0.0153830i
$780$	−5.32150e9			−0.401516
$781$	2.58941e9	+	1.46853e10i	0.194501	+	1.10307i
$782$	−2.43454e10	+	2.04282e10i	−1.82051	+	1.52759i
$783$	3.58012e9	−	1.30306e9i	0.266521	−	0.0970056i
$784$	−7.05476e9	−	2.56772e9i	−0.522848	−	0.190301i
$785$	−1.04664e10	−	8.78232e9i	−0.772240	−	0.647986i
$786$	3.18354e9	−	5.51405e9i	0.233847	−	0.405034i
$787$	1.07319e10	+	1.85882e10i	0.784812	+	1.35933i	0.929111	+	0.369800i	$0.120574\pi$
$787$	1.07319e10	+	1.85882e10i	0.784812	+	1.35933i	−0.144299	+	0.989534i	$0.546093\pi$
$788$	−5.52373e8	+	3.13266e9i	−0.0402153	+	0.228072i
$789$	−4.69764e9	+	2.66417e10i	−0.340495	+	1.93104i
$790$	6.72155e8	+	1.16421e9i	0.0485037	+	0.0840108i
$791$	−7.98724e9	+	1.38343e10i	−0.573824	+	0.993893i
$792$	−3.19803e8	−	2.68347e8i	−0.0228742	−	0.0191937i
$793$	−1.36549e10	−	4.96999e9i	−0.972374	−	0.353915i
$794$	6.83971e9	−	2.48945e9i	0.484915	−	0.176495i
$795$	9.09128e9	−	7.62849e9i	0.641712	−	0.538460i
$796$	−1.83031e9	−	1.03802e10i	−0.128626	−	0.729474i
$797$	−5.32150e9			−0.372332			−0.186166	−	0.982518i	$-0.559606\pi$
$797$	−5.32150e9			−0.372332			−0.186166	+	0.982518i	$0.559606\pi$
$798$	9.39174e9	−	1.67590e10i	0.654238	−	1.16745i
$799$	2.61220e10			1.81173
$800$	2.05930e8	+	1.16788e9i	0.0142201	+	0.0806464i
$801$	1.36424e9	−	1.14473e9i	0.0937943	−	0.0787027i
$802$	−1.15903e9	+	4.21854e8i	−0.0793389	+	0.0288770i
$803$	1.35880e9	+	4.94563e8i	0.0926085	+	0.0337067i
$804$	−5.36174e9	−	4.49903e9i	−0.363839	−	0.305297i
$805$	−1.81226e10	+	3.13893e10i	−1.22443	+	2.12078i
$806$	3.56183e9	+	6.16928e9i	0.239608	+	0.415013i
$807$	−1.03919e9	+	5.89351e9i	−0.0696042	+	0.394745i
$808$	7.53209e8	−	4.27166e9i	0.0502314	−	0.284877i
$809$	−4.24540e9	−	7.35326e9i	−0.281903	−	0.488270i	0.689951	−	0.723856i	$-0.257632\pi$
$809$	−4.24540e9	−	7.35326e9i	−0.281903	−	0.488270i	−0.971853	+	0.235587i	$0.924299\pi$
$810$	−4.30276e9	+	7.45261e9i	−0.284479	+	0.492732i
$811$	−2.00876e10	−	1.68555e10i	−1.32238	−	1.10961i	−0.985795	−	0.167950i	$-0.946285\pi$
$811$	−2.00876e10	−	1.68555e10i	−1.32238	−	1.10961i	−0.336580	−	0.941655i	$-0.609270\pi$
$812$	−3.89527e9	−	1.41776e9i	−0.255324	−	0.0929303i
$813$	−5.78719e9	+	2.10636e9i	−0.377703	+	0.137473i
$814$	8.45216e9	−	7.09220e9i	0.549265	−	0.460888i
$815$	−3.52213e8	−	1.99750e9i	−0.0227905	−	0.129251i
$816$	7.38400e9			0.475747
$817$	−2.85209e9	+	1.07963e9i	−0.182972	+	0.0692626i
$818$	−2.21097e10			−1.41236
$819$	−5.63358e8	−	3.19496e9i	−0.0358337	−	0.203223i
$820$	−6.90568e7	+	5.79456e7i	−0.00437379	+	0.00367005i
$821$	−4.39473e9	+	1.59955e9i	−0.277160	+	0.100878i	−0.476861	−	0.878979i	$-0.658225\pi$
$821$	−4.39473e9	+	1.59955e9i	−0.277160	+	0.100878i	0.199700	+	0.979857i	$0.436003\pi$
$822$	−1.67320e9	−	6.08996e8i	−0.105074	−	0.0382440i
$823$	−6.35543e9	−	5.33284e9i	−0.397416	−	0.333472i	0.422078	−	0.906560i	$-0.361301\pi$
$823$	−6.35543e9	−	5.33284e9i	−0.397416	−	0.333472i	−0.819494	+	0.573088i	$0.805745\pi$
$824$	2.81270e9	−	4.87173e9i	0.175137	−	0.303346i
$825$	3.00977e9	+	5.21307e9i	0.186614	+	0.323225i
$826$	−2.48945e9	+	1.41184e10i	−0.153700	+	0.871676i
$827$	5.43366e9	−	3.08158e10i	0.334059	−	1.89454i	−0.102271	−	0.994757i	$-0.532611\pi$
$827$	5.43366e9	−	3.08158e10i	0.334059	−	1.89454i	0.436330	−	0.899787i	$-0.356278\pi$
$828$	−8.39535e8	−	1.45412e9i	−0.0513964	−	0.0890212i
$829$	8.97232e9	−	1.55405e10i	0.546971	−	0.947381i	−0.451509	−	0.892266i	$-0.649114\pi$
$829$	8.97232e9	−	1.55405e10i	0.546971	−	0.947381i	0.998480	−	0.0551147i	$-0.0175524\pi$
$830$	1.33532e9	+	1.12046e9i	0.0810607	+	0.0680180i
$831$	−2.78862e10	−	1.01497e10i	−1.68572	−	0.613552i
$832$	2.02964e9	−	7.38729e8i	0.122176	−	0.0444686i
$833$	5.13624e10	−	4.30982e10i	3.07885	−	2.58346i
$834$	1.05368e9	+	5.97573e9i	0.0628968	+	0.356705i
$835$	−1.74228e9			−0.103566
$836$	6.45757e9	−	8.27011e7i	0.382250	−	0.00489541i
$837$	1.03612e10			0.610759
$838$	1.76391e9	+	1.00036e10i	0.103543	+	0.587223i
$839$	1.40061e10	−	1.17525e10i	0.818747	−	0.687011i	−0.133931	−	0.990991i	$-0.542760\pi$
$839$	1.40061e10	−	1.17525e10i	0.818747	−	0.687011i	0.952678	+	0.303980i	$0.0983156\pi$
$840$	7.91345e9	−	2.88026e9i	0.460668	−	0.167670i
$841$	1.47256e10	+	5.35968e9i	0.853664	+	0.310708i
$842$	−8.92553e9	−	7.48941e9i	−0.515278	−	0.432370i
$843$	−3.77738e8	+	6.54261e8i	−0.0217167	+	0.0376145i
$844$	−1.65044e9	−	2.85865e9i	−0.0944933	−	0.163667i
$845$	1.82723e8	−	1.03627e9i	0.0104182	−	0.0590847i
$846$	−2.39653e8	+	1.35914e9i	−0.0136078	+	0.0771734i
$847$	6.59752e9	+	1.14272e10i	0.373069	+	0.646174i
$848$	−2.40846e9	+	4.17158e9i	−0.135630	+	0.234917i
$849$	−2.09598e10	−	1.75874e10i	−1.17547	−	0.986333i
$850$	−9.95244e9	−	3.62239e9i	−0.555857	−	0.202316i
$851$	4.17003e10	−	1.51777e10i	2.31945	−	0.844212i
$852$	1.06746e10	−	8.95709e9i	0.591309	−	0.496167i
$853$	1.65365e9	+	9.37830e9i	0.0912265	+	0.517371i	0.995839	+	0.0911353i	$0.0290496\pi$
$853$	1.65365e9	+	9.37830e9i	0.0912265	+	0.517371i	−0.904612	+	0.426236i	$0.859839\pi$
$854$	2.29959e10			1.26342
$855$	2.75473e8	+	1.45321e9i	0.0150729	+	0.0795144i
$856$	−5.60660e9			−0.305521
$857$	2.16677e9	+	1.22883e10i	0.117592	+	0.666900i	0.985434	+	0.170059i	$0.0543957\pi$
$857$	2.16677e9	+	1.22883e10i	0.117592	+	0.666900i	−0.867842	+	0.496841i	$0.834493\pi$
$858$	8.39850e9	−	7.04718e9i	0.453938	−	0.380899i
$859$	9.13853e9	−	3.32615e9i	0.491927	−	0.179047i	−0.0841327	−	0.996455i	$-0.526812\pi$
$859$	9.13853e9	−	3.32615e9i	0.491927	−	0.179047i	0.576059	+	0.817408i	$0.304590\pi$
$860$	−1.25619e9	−	4.57214e8i	−0.0673456	−	0.0245118i
$861$	−4.23223e8	−	3.55126e8i	−0.0225974	−	0.0189614i
$862$	9.39403e9	−	1.62709e10i	0.499547	−	0.865241i
$863$	1.03404e10	+	1.79101e10i	0.547646	+	0.948552i	0.998435	+	0.0559209i	$0.0178095\pi$
$863$	1.03404e10	+	1.79101e10i	0.547646	+	0.948552i	−0.450789	+	0.892631i	$0.648857\pi$
$864$	5.45518e8	−	3.09379e9i	0.0287747	−	0.163189i
$865$	7.21676e7	−	4.09283e8i	0.00379128	−	0.0215014i
$866$	−4.30594e9	−	7.45811e9i	−0.225297	−	0.390226i
$867$	−2.28620e10	+	3.95982e10i	−1.19137	+	2.06352i
$868$	−8.63582e9	−	7.24631e9i	−0.448213	−	0.376095i
$869$	−2.60255e9	−	9.47250e8i	−0.134533	−	0.0489661i
$870$	3.01480e9	−	1.09730e9i	0.155218	−	0.0564947i
$871$	1.40069e10	−	1.17532e10i	0.718255	−	0.602688i
$872$	8.32061e8	+	4.71885e9i	0.0424959	+	0.241006i
$873$	8.83293e8			0.0449319
$874$	2.45197e10	+	8.57046e9i	1.24229	+	0.434224i
$875$	−3.81540e10			−1.92536
$876$	−2.34644e8	−	1.33073e9i	−0.0117936	−	0.0668846i
$877$	−2.07713e10	+	1.74292e10i	−1.03983	+	0.872525i	−0.991988	−	0.126330i	$-0.959680\pi$
$877$	−2.07713e10	+	1.74292e10i	−1.03983	+	0.872525i	−0.0478463	+	0.998855i	$0.515236\pi$
$878$	2.11031e10	−	7.68089e9i	1.05224	−	0.382984i
$879$	−5.48007e9	−	1.99458e9i	−0.272160	−	0.0990583i
$880$	2.16863e9	+	1.81970e9i	0.107274	+	0.0900139i
$881$	−1.85066e10	+	3.20544e10i	−0.911825	+	1.57933i	−0.100342	+	0.994953i	$0.531994\pi$
$881$	−1.85066e10	+	3.20544e10i	−0.911825	+	1.57933i	−0.811484	+	0.584375i	$0.801340\pi$
$882$	1.77120e9	+	3.06781e9i	0.0869217	+	0.150553i
$883$	−2.05608e8	+	1.16606e9i	−0.0100503	+	0.0569979i	−0.989420	−	0.145076i	$-0.953657\pi$
$883$	−2.05608e8	+	1.16606e9i	−0.0100503	+	0.0569979i	0.979370	+	0.202074i	$0.0647683\pi$
$884$	−3.34965e9	+	1.89968e10i	−0.163086	+	0.924905i
$885$	−5.54786e9	−	9.60917e9i	−0.269044	−	0.465998i
$886$	−8.24356e9	+	1.42783e10i	−0.398196	+	0.689695i
$887$	1.31683e10	+	1.10495e10i	0.633575	+	0.531633i	0.902038	−	0.431657i	$-0.142071\pi$
$887$	1.31683e10	+	1.10495e10i	0.633575	+	0.531633i	−0.268462	+	0.963290i	$0.586515\pi$
$888$	−9.68877e9	−	3.52642e9i	−0.464326	−	0.169001i
$889$	−6.61905e10	+	2.40914e10i	−3.15965	+	1.15002i
$890$	−9.25108e9	+	7.76258e9i	−0.439873	+	0.369097i
$891$	−3.07866e9	−	1.74599e10i	−0.145811	−	0.826933i
$892$	2.80304e9			0.132237
$893$	−1.09107e10	−	1.83510e10i	−0.512709	−	0.862344i
$894$	3.03420e8			0.0142024
$895$	−1.86358e9	−	1.05689e10i	−0.0868896	−	0.492776i
$896$	−2.61838e9	+	2.19708e9i	−0.121606	+	0.102040i
$897$	4.14356e10	−	1.50813e10i	1.91690	−	0.697695i
$898$	1.72479e9	+	6.27772e8i	0.0794820	+	0.0289291i
$899$	−3.29001e9	−	2.76064e9i	−0.151021	−	0.126722i
$900$	2.79782e8	−	4.84597e8i	0.0127930	−	0.0221581i
$901$	−2.15098e10	−	3.72560e10i	−0.979712	−	1.69691i
$902$	3.22505e7	−	1.82902e8i	0.00146323	−	0.00829841i
$903$	1.42266e9	−	8.06829e9i	0.0642974	−	0.364649i
$904$	2.50909e9	+	4.34588e9i	0.112961	+	0.195654i
$905$	−1.07937e10	+	1.86953e10i	−0.484062	+	0.838420i
$906$	1.96021e10	+	1.64481e10i	0.875698	+	0.734798i
$907$	1.52676e10	+	5.55695e9i	0.679430	+	0.247292i	0.658603	−	0.752491i	$-0.271148\pi$
$907$	1.52676e10	+	5.55695e9i	0.679430	+	0.247292i	0.0208273	+	0.999783i	$0.493370\pi$
$908$	1.79419e10	−	6.53033e9i	0.795370	−	0.289491i
$909$	−1.56784e9	+	1.31557e9i	−0.0692352	+	0.0580953i
$910$	3.82021e9	+	2.16655e10i	0.168051	+	0.953067i
$911$	1.46991e9			0.0644135			0.0322067	−	0.999481i	$-0.489747\pi$
$911$	1.46991e9			0.0644135			0.0322067	+	0.999481i	$0.489747\pi$
$912$	−3.08416e9	−	5.18736e9i	−0.134634	−	0.226446i
$913$	−3.59123e9			−0.156169
$914$	−1.44721e9	−	8.20755e9i	−0.0626932	−	0.355551i
$915$	−1.36341e10	+	1.14403e10i	−0.588371	+	0.493702i
$916$	−1.32498e10	+	4.82252e9i	−0.569606	+	0.207320i
$917$	−2.47348e10	−	9.00273e9i	−1.05929	−	0.385551i
$918$	2.14926e10	+	1.80344e10i	0.916935	+	0.769400i
$919$	3.41048e9	−	5.90712e9i	0.144948	−	0.251057i	−0.784406	−	0.620248i	$-0.787032\pi$
$919$	3.41048e9	−	5.90712e9i	0.144948	−	0.251057i	0.929353	+	0.369191i	$0.120365\pi$
$920$	5.69300e9	+	9.86056e9i	0.241037	+	0.417488i
$921$	−1.74601e9	+	9.90212e9i	−0.0736441	+	0.417657i
$922$	5.79251e9	−	3.28510e10i	0.243393	−	1.38035i
$923$	1.82015e10	+	3.15258e10i	0.761904	+	1.31966i
$924$	−8.67488e9	+	1.50253e10i	−0.361753	+	0.626574i
$925$	1.13289e10	+	9.50610e9i	0.470644	+	0.394917i
$926$	−1.80835e10	−	6.58185e9i	−0.748417	−	0.272401i
$927$	−2.49425e9	+	9.07834e8i	−0.102840	+	0.0374307i
$928$	−9.97531e8	+	8.37028e8i	−0.0409740	+	0.0343813i
$929$	−6.88352e8	−	3.90384e9i	−0.0281680	−	0.159748i	0.967479	−	0.252950i	$-0.0814009\pi$
$929$	−6.88352e8	−	3.90384e9i	−0.0281680	−	0.159748i	−0.995647	+	0.0932019i	$0.970290\pi$
$930$	8.72511e9			0.355697
$931$	−5.17302e10	−	1.80815e10i	−2.10097	−	0.734361i
$932$	1.31391e10			0.531629
$933$	5.37461e9	+	3.04809e10i	0.216651	+	1.22869i
$934$	−3.11279e9	+	2.61194e9i	−0.125007	+	0.104894i
$935$	−2.37581e10	+	8.64726e9i	−0.950543	+	0.345969i
$936$	−9.57681e8	−	3.48567e8i	−0.0381729	−	0.0138938i
$937$	−2.22176e10	−	1.86428e10i	−0.882283	−	0.740323i	0.0843642	−	0.996435i	$-0.473114\pi$
$937$	−2.22176e10	−	1.86428e10i	−0.882283	−	0.740323i	−0.966647	+	0.256112i	$0.917559\pi$
$938$	−1.44679e10	+	2.50591e10i	−0.572393	+	0.991414i
$939$	1.30790e10	+	2.26534e10i	0.515518	+	0.892904i
$940$	1.62512e9	−	9.21651e9i	0.0638172	−	0.361925i
$941$	−8.07469e8	+	4.57938e9i	−0.0315909	+	0.179161i	−0.996521	−	0.0833478i	$-0.973439\pi$
$941$	−8.07469e8	+	4.57938e9i	−0.0315909	+	0.179161i	0.964930	+	0.262509i	$0.0845499\pi$
$942$	−1.31521e10	−	2.27801e10i	−0.512645	−	0.887927i
$943$	3.73487e8	−	6.46899e8i	0.0145039	−	0.0251215i
$944$	3.44992e9	+	2.89482e9i	0.133477	+	0.112001i
$945$	3.00682e10	+	1.09439e10i	1.15904	+	0.421854i
$946$	2.58802e9	−	9.41962e8i	0.0993913	−	0.0361755i
$947$	1.55952e10	−	1.30860e10i	0.596715	−	0.500704i	−0.293673	−	0.955906i	$-0.594878\pi$
$947$	1.55952e10	−	1.30860e10i	0.596715	−	0.500704i	0.890388	+	0.455202i	$0.150433\pi$
$948$	4.49420e8	+	2.54879e9i	0.0171326	+	0.0971638i
$949$	3.53001e9			0.134074
$950$	1.61217e9	+	8.50472e9i	0.0610069	+	0.321831i
$951$	−8.31123e9			−0.313353
$952$	−5.30084e9	−	3.00626e10i	−0.199120	−	1.12927i
$953$	1.20790e10	−	1.01355e10i	0.452069	−	0.379331i	−0.388134	−	0.921603i	$-0.626880\pi$
$953$	1.20790e10	−	1.01355e10i	0.452069	−	0.379331i	0.840203	+	0.542272i	$0.182436\pi$
$954$	2.13579e9	−	7.77362e8i	0.0796413	−	0.0289871i
$955$	1.58764e10	+	5.77855e9i	0.589849	+	0.214688i
$956$	−2.57404e9	−	2.15987e9i	−0.0952823	−	0.0799514i
$957$	−3.30489e9	+	5.72423e9i	−0.121889	+	0.211118i
$958$	2.27868e9	+	3.94680e9i	0.0837346	+	0.145033i
$959$	−1.27825e9	+	7.24931e9i	−0.0468005	+	0.265419i
$960$	4.59379e8	−	2.60527e9i	0.0167580	−	0.0950392i
$961$	7.91634e9	+	1.37115e10i	0.287735	+	0.498371i
$962$	1.34676e10	−	2.33265e10i	0.487727	−	0.844768i
$963$	2.02654e9	+	1.70047e9i	0.0731245	+	0.0613588i
$964$	−9.48552e8	−	3.45245e8i	−0.0341029	−	0.0124124i
$965$	−1.21185e9	+	4.41078e8i	−0.0434114	+	0.0158005i
$966$	−5.34549e10	+	4.48540e10i	−1.90795	+	1.60096i
$967$	−4.41418e9	−	2.50341e10i	−0.156985	−	0.890305i	−0.956949	−	0.290257i	$-0.906259\pi$
$967$	−4.41418e9	−	2.50341e10i	−0.156985	−	0.890305i	0.799964	−	0.600048i	$-0.204852\pi$
$968$	4.14506e9			0.146882
$969$	5.38932e10	−	6.90201e8i	1.90283	−	0.0243693i
$970$	−5.98972e9			−0.210720
$971$	8.03371e9	+	4.55614e10i	0.281611	+	1.59709i	0.717147	+	0.696922i	$0.245448\pi$
$971$	8.03371e9	+	4.55614e10i	0.281611	+	1.59709i	−0.435537	+	0.900171i	$0.643441\pi$
$972$	−2.41205e9	+	2.02395e9i	−0.0842470	+	0.0706916i
$973$	2.35726e10	−	8.57973e9i	0.820376	−	0.298592i
$974$	2.25490e10	+	8.20715e9i	0.781934	+	0.284601i
$975$	1.12570e10	+	9.44575e9i	0.388961	+	0.326377i
$976$	3.61194e9	−	6.25606e9i	0.124356	−	0.215391i
$977$	−4.86634e7	−	8.42875e7i	−0.00166944	−	0.00289156i	0.865189	−	0.501445i	$-0.167198\pi$
$977$	−4.86634e7	−	8.42875e7i	−0.00166944	−	0.00289156i	−0.866859	+	0.498554i	$0.833865\pi$
$978$	6.78092e8	−	3.84565e9i	0.0231794	−	0.131457i
$979$	4.32038e9	−	2.45021e10i	0.147158	−	0.834572i
$980$	−1.20108e10	−	2.08032e10i	−0.407642	−	0.706057i
$981$	1.13046e9	−	1.95802e9i	0.0382309	−	0.0662179i
$982$	−2.24226e10	−	1.88148e10i	−0.755606	−	0.634029i
$983$	2.28184e10	+	8.30522e9i	0.766210	+	0.278878i	0.695410	−	0.718613i	$-0.255223\pi$
$983$	2.28184e10	+	8.30522e9i	0.766210	+	0.278878i	0.0707998	+	0.997491i	$0.477445\pi$
$984$	−1.63088e8	+	5.93591e7i	−0.00545680	+	0.00198611i
$985$	−7.79687e9	+	6.54235e9i	−0.259952	+	0.218126i
$986$	−2.01947e9	−	1.14530e10i	−0.0670917	−	0.380496i
$987$	5.73558e10			1.89875
$988$	1.47446e10	−	5.58143e9i	0.486388	−	0.184118i
$989$	1.10770e10			0.364111
$990$	−2.31955e8	−	1.31548e9i	−0.00759767	−	0.0430885i
$991$	1.47258e9	−	1.23564e9i	0.0480641	−	0.0403305i	−0.618439	−	0.785833i	$-0.712235\pi$
$991$	1.47258e9	−	1.23564e9i	0.0480641	−	0.0403305i	0.666503	+	0.745502i	$0.267790\pi$
$992$	−3.32779e9	+	1.21122e9i	−0.108234	+	0.0393941i
$993$	2.25596e10	+	8.21103e9i	0.731155	+	0.266119i
$994$	−4.41302e10	−	3.70296e10i	−1.42523	−	1.19591i
$995$	1.68627e10	−	2.92071e10i	0.542684	−	0.939957i
$996$	1.67796e9	+	2.90632e9i	0.0538115	+	0.0932042i
$997$	2.37881e9	−	1.34909e10i	0.0760198	−	0.431130i	−0.922916	−	0.385002i	$-0.874201\pi$
$997$	2.37881e9	−	1.34909e10i	0.0760198	−	0.431130i	0.998936	−	0.0461279i	$-0.0146882\pi$
$998$	−6.02200e9	+	3.41525e10i	−0.191771	+	1.08759i
$999$	−1.95882e10	−	3.39278e10i	−0.621607	−	1.07665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.b.9.5	✓	36
19.17	even	9	inner	38.8.e.b.17.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.b.9.5	✓	36	1.1	even	1	trivial
38.8.e.b.17.5	yes	36	19.17	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38919 - 7.87846i) q^{2} +(37.7512 - 31.6770i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-192.429 - 70.0383i) q^{5} +(-302.010 - 253.416i) q^{6} +(-814.928 + 1411.50i) q^{7} +(256.000 + 443.405i) q^{8} +(41.9510 - 237.916i) q^{9} +O(q^{10})\)	\(q+(-1.38919 - 7.87846i) q^{2} +(37.7512 - 31.6770i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-192.429 - 70.0383i) q^{5} +(-302.010 - 253.416i) q^{6} +(-814.928 + 1411.50i) q^{7} +(256.000 + 443.405i) q^{8} +(41.9510 - 237.916i) q^{9} +(-284.475 + 1613.34i) q^{10} +(-1687.55 - 2922.93i) q^{11} +(-1576.98 + 2731.41i) q^{12} +(-6311.72 - 5296.16i) q^{13} +(12252.5 + 4459.55i) q^{14} +(-9483.02 + 3451.54i) q^{15} +(3137.72 - 2632.86i) q^{16} +(6352.22 + 36025.2i) q^{17} -1932.69 q^{18} +(22655.0 - 19509.6i) q^{19} +13105.8 q^{20} +(13947.5 + 79100.2i) q^{21} +(-20683.9 + 17355.8i) q^{22} +(-102048. + 37142.3i) q^{23} +(23710.1 + 8629.75i) q^{24} +(-27723.8 - 23263.0i) q^{25} +(-32957.4 + 57084.0i) q^{26} +(47935.7 + 83027.0i) q^{27} +(18113.4 - 102726. i) q^{28} +(6900.69 - 39135.8i) q^{29} +(40366.5 + 69916.8i) q^{30} +(54036.9 - 93594.6i) q^{31} +(-25101.7 - 21062.9i) q^{32} +(-156297. - 56887.4i) q^{33} +(274999. - 100091. i) q^{34} +(255674. - 214536. i) q^{35} +(2684.86 + 15226.6i) q^{36} -408636. q^{37} +(-185177. - 151384. i) q^{38} -406041. q^{39} +(-18206.4 - 103254. i) q^{40} +(-5269.18 + 4421.36i) q^{41} +(603812. - 219770. i) q^{42} +(-95849.5 - 34886.4i) q^{43} +(165471. + 138847. i) q^{44} +(-24735.8 + 42843.6i) q^{45} +(434387. + 752381. i) q^{46} +(124000. - 703238. i) q^{47} +(35051.5 - 198787. i) q^{48} +(-916445. - 1.58733e6i) q^{49} +(-144763. + 250737. i) q^{50} +(1.38098e6 + 1.15878e6i) q^{51} +(495518. + 180354. i) q^{52} +(-1.10509e6 + 402218. i) q^{53} +(587534. - 492999. i) q^{54} +(120017. + 680649. i) q^{55} -834487. q^{56} +(237247. - 1.45415e6i) q^{57} -317916. q^{58} +(190926. + 1.08279e6i) q^{59} +(494760. - 415153. i) q^{60} +(1.65728e6 - 603201. i) q^{61} +(-812449. - 295707. i) q^{62} +(301630. + 253098. i) q^{63} +(-131072. + 227023. i) q^{64} +(843621. + 1.46119e6i) q^{65} +(-231060. + 1.31041e6i) q^{66} +(-385359. + 2.18548e6i) q^{67} +(-1.17059e6 - 2.02752e6i) q^{68} +(-2.67586e6 + 4.63473e6i) q^{69} +(-2.04540e6 - 1.71629e6i) q^{70} +(-4.15172e6 - 1.51110e6i) q^{71} +(116232. - 42305.2i) q^{72} +(-328198. + 275391. i) q^{73} +(567671. + 3.21942e6i) q^{74} -1.78351e6 q^{75} +(-935427. + 1.66921e6i) q^{76} +5.50094e6 q^{77} +(564067. + 3.19898e6i) q^{78} +(628607. - 527464. i) q^{79} +(-788188. + 286877. i) q^{80} +(4.93616e6 + 1.79662e6i) q^{81} +(42153.4 + 35370.9i) q^{82} +(532018. - 921481. i) q^{83} +(-2.57025e6 - 4.45181e6i) q^{84} +(1.30080e6 - 7.37719e6i) q^{85} +(-141698. + 803610. i) q^{86} +(-979195. - 1.69602e6i) q^{87} +(864027. - 1.49654e6i) q^{88} +(5.64701e6 + 4.73840e6i) q^{89} +(371905. + 135362. i) q^{90} +(1.26191e7 - 4.59298e6i) q^{91} +(5.32416e6 - 4.46750e6i) q^{92} +(-924841. - 5.24504e6i) q^{93} -5.71269e6 q^{94} +(-5.72589e6 + 2.16749e6i) q^{95} -1.61483e6 q^{96} +(634897. + 3.60068e6i) q^{97} +(-1.12326e7 + 9.42527e6i) q^{98} +(-766205. + 278876. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * q^99

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